Organized by: Zhilan Feng (National Science Foundation), John W Glasser, The US Centers for Disease Control and Prevention (CDC)

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. John W Glasser The US Centers for Disease Control and Prevention (CDC)
   "Validating a SARS-CoV-2 transmission model"
During the COVID-19 pandemic, we endeavored to keep pace with understanding of biological phenomena that might affect SARS-CoV-2 transmission by modifying SEIR metapopulation models structured via age, location, or strain. With probabilities of infection on contact and initial conditions from a serial, cross-sectional survey of antibodies to nucleocapsid protein among commercial laboratory clients throughout the United States and all save one other parameter from the literature, our age- and location-structured model reproduced seroprevalence from this and another nationwide survey, of antibodies to spike as well as nucleocapsid protein among blood-donors, remarkably well. Because fit parameters are conditional on model formulae and other parameter values, we recommend that mechanistic modelers base theirs on first principles, estimate them from accurate independent observations, or source them from the primary, not the modeling literature. In this talk, I will describe our descriptive model of seroprevalence by age and time and then our calculation, via first principles, of the age-specific forces of infection, attack rates and -- given information from a contact study -- probabilities of infection on contact. Because those parameters were not estimated by fitting our transmission model to any observations, others could use them too.
2. Wendy S Parker Virginia Tech
   "Testing the adequacy-for-purpose of dynamical models"
Dynamical models, especially mechanistic ones, are often viewed as “hypotheses” about the workings of a target system. Such hypotheses, however, are often known to be false from the outset, insofar as models are known to involve various simplifications, idealizations, and omissions. A more coherent perspective instead views scientific models as representational tools, the evaluation of which is concerned with their adequacy or fitness for particular purposes of interest. Adopting this perspective, stringent testing is still an aim of model evaluation, but what is ultimately tested is not the model itself, but a hypothesis about its adequacy- or fitness-for-purpose. Ideally, model evaluation is carried out such that, if the model is inadequate for the purpose of interest, then the testing procedure is very likely to reveal that inadequacy.
3. Michael Y. Li University of Alberta
   "Why do models calibrated with data need to be validated?"
Mechanistic models based on dynamical system theory are natural for making predictions. There is a general belief that these models are constructed based on the best available science, they are inherently valid. But are they? Reliable quantitative model predictions rely on both the model structure (mechanisms incorporated) and the model parameters. Models with the same structure but different parameter values can make different finite-time quantitative predictions. Model parameter values are critical for accurate predictions. When parameter values of an epidemic model using the trusted SEIAR structure for COVID-19 are estimated from fitting model outputs to COVID-19 data, and these parameter values allow an excellent fitting between model outputs and the data, would this mean the calibrated model is validated, can be trusted for scenario analysis, and for making recommendations to public health decision makers? I will use examples to show that epidemic models calibrated from data are prone to the following failures: (1) fail the cross-validation test, (2) suffer from over-fitting, and (3) over-project the final size. I will provide some of the underlying reasons for these failings. I will also present a study on estimating the proportion of infected population of COVID-19, using identified-case data for model training and reserving the seroprevalence data for model validation.
4. Marie Betsy Varughese Institute of Health Economics
   "Real-time Validation of Model Projections of Seasonal Influenza in Alberta"
Modelling efforts during the COVID-19 pandemic highlighted the challenges that arose with making accurate and validating projections. The difficulty or near impossibility to accurately predict the peak time and other epidemic indicators using standard mathematical models with constate rate parameters have been stated previously in literature. This talk will describe an age-stratified Susceptible-Infectious-Recovered (SIR) deterministic model used to describe influenza transmission dynamics in Alberta. We will describe our validation approach and compare the performance of making accurate model projections based on our assumptions of case detection when calibrating to surveillance data between 2016 and 2019. In addition, we will present more recent real-time influenza model projections for cases and hospitalizations for the 2023-2024 respiratory virus seasons and discuss how we present these findings to decision and policy makers.

Organized by: Iain Moyles (York University), Rebecca Tyson, University of British Columbia Okanagan

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Iain Moyles York University
   "Fear dynamics in a mathematical model of disease transmission"
We explore a mathematical model of disease transmission with a fearful compartment. Susceptible individuals become afraid by either interacting with individuals who are already afraid or those who are infected. Individuals who are afraid take protective measures via contact reductions to reduce risk of transmission. Individuals can lose fear naturally over time or because they see people recovering from the disease. We consider two scenarios of the model, one where fear is obtained at a slower rate than disease spread and one where it is comparable. In the former we show that behavioural change cannot impact disease outcome, but in the latter, we observe that sufficient behavioural intervention can reduce disease impact. However, response to recovery can induce a bifurcation where contact reduction cannot mitigate disease spread. We identify this bifurcation and demonstrate its implication on disease dynamics and final size.
2. Md. Mijanur Rahman University of British Columbia Okanagan
   "The role of opinion dynamics in generating multiple epidemic waves"
We develop and rigorously analyze a coupled opinion-disease framework in which the population is partitioned into two susceptible classes that differ in their infection rates and are linked by opinion switching. We show that the model preserves classic SIR-type dynamics for the total susceptible population but embeds a feedback loop through a time-varying effective transmission rate that depends on the opinion proportions. We define an effective reproduction rate based on the transmission rate and establish explicit criteria for epidemic peaks in terms of its sign changes. Two asymptotic regimes are examined using the scaled base opinion-switching rate. In the slow switching limit, opinion exchange freezes and guarantees at most one infection wave. In the fast switching limit, the opinion distribution equilibrates instantaneously to a quasi-steady state, which again leads to a single wave. Extending the model to Hill-type, infection-dependent switching rates yields the same one-wave result in both asymptotic limits. These findings imply that neither vanishingly slow nor extremely rapid opinion change, as modelled here, can sustain recurrent outbreaks. Repeated waves in this framework must arise from intermediate switching speeds or necessitate the inclusion of additional mechanisms not considered in these asymptotic limits. The work highlights the speed of opinion change as a potential public health leverage point.
3. Azadeh Aghaeeyan Brock University
   "Understanding the Decision-Making of Late COVID-19 Vaccine Adopters"
Individuals responded differently to the COVID-19 vaccination campaign: some were early adopters, others delayed vaccination, and some refused it altogether. Despite the important role of late adopters in pandemic control, their behaviour remains understudied. We propose a mechanistic model that divides late adopters based on their decision-making strategies into two types: success-based learners, who are influenced by others’ vaccination experiences, and myopic rationalists, who receive their shots when the perceived benefit of vaccination outweighs the cost. The model also accounts for possible shifts in vaccination perception triggered by impactful events. Using a Bayesian framework, we fit the model to weekly COVID-19 vaccine uptake data from U.S. states, stratified by age and sex. Our results suggest that late adopters mainly behaved as success-based learners and that perception shifts varied across events—some increased and others reduced the perceived value of vaccination. These findings are a step toward tailoring vaccine promotion communication strategies to late adopters.
4. Ariel Greiner
   "Can tourism drive effective coral reef management? A modelling study."
Coral reefs are some of the most threatened ecosystems on the planet but also some of the most important, hosting upwards of 25% of marine biodiversity while also providing food and livelihood to almost 1 billion people. Coral reefs are also connected together into reef networks by coral larval dispersal, meaning that management or damage at one reef may have consequences for any reefs it is connected to. For this reason, coral reef management is of interest to many industries (e.g., fisheries, tourism) and governments. The potential impact of tourism in the context of coral reef management is unclear, as tourism is a source of damage for reefs but may also be a source of income that motivates conservation actors to keep reefs healthy for future tourists. Tourism groups also often focus on a subset of coral reefs, meaning that any management initiatives driven by tourism income would also only be focused on a subset of coral reefs in a reef network. We develop a socio-ecological model composed of a system of differential equations. This model represents a network of coral reefs visited by tourists to determine whether tourism income could help sustain a healthy network of coral reefs into the future. We explore this question under a variety of different tourism paradigms, management methods (coral restoration, fisheries management) and network types. Overall, we find that management funded by tourism can help counteract tourism damage, but is unable to save reefs that are unhealthy (low initial coral cover, high fishing). Management also has limited potential to help connected reefs in the network. This study demonstrates the limited effectiveness of tourism to drive coral reef conservation and instead encourages active investment in management methods that focus on the entire reef network.

Organized by: Zhilan Feng (National Science Foundation), John W Glasser, The US Centers for Disease Control and Prevention (CDC)

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Junling Ma University of Victoria
   "Assess the effectiveness of Contact Tracing during the early stage of a pandemic"
Contact tracing is an important intervention measure to control infectious diseases. We present a new approach that tracks contacts in a randomly mixed population, which allow us to precisely model the contact tracing process. The model resulting from this new approach allows us to study the effect of contact tracing and isolation of diagnosed patients on the control reproduction number and number of infected individuals. However, we found that case counts alone during an early stage of an outbreak before susceptible population have been depleted is not sufficient to identify key contact tracing parameters such as coverage probability (the fraction of contacts successfully tracked) and testing rate. We need the reason that a patient is tested for diagnosis, i.e., whether they are quarantined and showing symptom, or voluntarily tested due to symptom, or contact tracing while showing symptom. We then apply our model to estimate the effect of contact tracing on the basic reproduction number and epidemic size in Ontario, Canada.
2. Sen Pei Columbia University
   "Addressing the challenge of imperfect observation processes in epidemic modeling"
Mathematical models calibrated to infectious disease data are widely used to understand epidemic dynamics and inform public health policy. However, real-world surveillance data often suffer from limitations due to imperfect observation processes, posing significant challenges for accurate modeling and inference. In this talk, I will highlight key challenges in epidemic modeling arising from imperfect data, present several studies that address these issues, and discuss promising directions for future research.
3. Troy Day Queens University
   "Modelling the distribution of fitness effects of new mutations"
The distribution of fitness effects of new mutations is key to our understanding of many evolutionary processes. Theoreticians have developed several models to help understand the patterns seen in data and many of these models match the data extremely well. Here we argue that this excellent match between models and data provides very weak evidence for their explanatory power. To do so we prove that even randomly chosen models make predictions that are indistinguishable from empirical data. This suggests that other analyses are required to properly assess models for the distribution of fitness effects of mutations and we provide some suggestions as to how this might be done. This is joint work with Olivier Cotto.
4. Zhilan Feng National Science Foundation
   "Mechanistic models are hypotheses"
Science involves perceiving patterns (events that are repeated) in observations, hypothesizing causal explanations (underlying processes), and testing them. Mathematical models either describe or provide explanations for patterns. The equations of descriptive models have convenient mathematical properties while those of mechanistic ones correspond to processes. The parameters of descriptive models are fit to observations by choosing values that minimize discrepant predictions. Because mechanistic models are hypotheses about the processes underlying patterns, their parameters should not be fit, but rather, based insofar as possible on first principles or estimated independently. The precision of mathematics facilitates comparing the predictions of mechanistic models to the patterns that they purport to explain and, until concordant, identifying and remedying the cause(s) of disparities.

Organized by: Abba Gumel (University of Maryland), Alex Safsten, Alice Oveson (both University of Maryland)

Note: this minisymposia has multiple sessions. The other sessions are: Part-2, and Part-3.

1. Navid Ghaffarzadegan Virginia Tech
   "Pandemics and People: Modeling Outbreaks with Behavior in the Loop"
From social distancing and vaccination in response to the perceived risk of infection to changes in Non-Pharmaceutical Interventions under economic pressures, human responses alter the outcomes of an epidemic outbreak. While recognized in theory, this realization is not reflected in current infectious disease models at large. A grand challenge for scientists is to incorporate more realistic behavioral assumptions about human response and to couple human behavior models and epidemic models to represent change in human behavior endogenously (within epidemic models). In a series of studies, we show that the endogenous representation of human behavior: 1) improves the accuracy of long-term projections, 2) sheds light on several challenging puzzles such as early convergence to the reproductive number of one and the observed large variations in mortality rates across different regions, and 3) offers a different perspective on the health vs. economy tradeoff during a pandemic. We tested the models using detailed epidemiological and behavioral data from over 100 countries and 50 US regions, covering several waves of the pandemic over time.
2. Jane Heffernan York University
   "Modelling Positive and Negative Behaviour Change"
During an infectious disease outbreak, individuals can change their behaviour so as to minimize infection risk. Behaviour relaxation can also occur. We have developed models of increasing and decreasing behaviour change. We analyze the outcomes of behaviour change with respect to vaccine uptake and disease incidence and prevalence. COVID-19 is used as an example.
3. Sefah Frimpong University of Waterloo
   "COVID-19 Coupled Behaviour-Disease Model"
Mathematical models have been widely used to understand the dynamics of diseases from infectious diseases to oncology. Many infectious disease models have generally helped to understand the behaviour of diseases and in making predictions. However, recent data shows that the dynamics of these diseases are influenced by the behaviour of the host population. With evidence of imitation dynamics amongst the host population affecting the transmission of the disease. This work establishes that coupled behaviour-disease models give more information about the disease and improve the predictive powers of the models. We illustrate this concept by applying a formulated coupled behaviour-disease model for the first year of the COVID-19 virus from selected countries and cities while parameter estimation is performed using an Approximate Bayesian Computation (ABC) approach. We examine the predictive power of a conventional deterministic SIR model and a coupled behaviour-disease model which takes into account the seasonality of the COVID-19 virus. Using an adjusted AIC statistical measure for model performance, we obtained a similar performance for both models with respect to fitting but observed the coupled model outperformed the disease model in forecasting. Also, the peak magnitude and duration for the second peak within the prediction period had the coupled model match closely with the data unlike the disease model.
4. Binod Pant Northeastern University
   "Analyzing human behavior data and modeling the impact of human behavior on SARS-CoV-2 transmission dynamics"
The COVID-19 pandemic not only has profoundly impacted global health and socioeconomic systems, but has also significantly impacted human behavior toward adherence (or lack thereof) to public health intervention and mitigation measures implemented in communities around the world. However, a relatively small number of epidemiological models have attempted to assess the impact of human behavior on the dynamics of SARS-CoV-2 transmission. In addition, detailed characterizations of how population-level behaviors change over time during multiple disease outbreaks and spatial resolutions are not yet widely available. In this talk, a behavior-epidemiology model that incorporates multiple mechanisms of behavior change is presented. Data from 431,211 survey responses collected in the United States, between April 2020 and June 2022, are used to provide a description of how human behavior fluctuated during the first two years of the COVID-19 pandemic.

Organized by: Michael A. Robert (Virginia Tech)

1. Stacey Smith? University of Ottawa
   "Could COVID-19 mask and vaccine mandates have made a difference if they were rolled out earlier?"
Hospitalizations and deaths due to COVID-19 in Canada declined after the first wave, thanks to nonpharmaceutical interventions and the vaccination campaign starting in December 2020, despite the emergence of highly contagious variants. We used an age-structured extended Susceptible-Exposed-Infected-Recovered compartment model to mimic the transmission of COVID-19 in Ontario from March 1, 2020 to May 31, 2021. We examined several counterfactual scenarios: 1. No mask mandates; 2. No vaccination; 3. Instigating the mask mandate a month earlier; 4. Rolling out the vaccine a month earlier. A one-month-earlier vaccination program could have significantly decreased the number of cases and hospitalizations, but one-month-earlier mask mandates would not have. It follows that the mandates that were implemented in practice were not optimal, but mostly performed well. Our model demonstrates that mask mandates played a vital role in saving lives in the first wave of the COVID-19 outbreak and that the vaccination program was crucial to averting subsequent cases and hospitalizations after it was implemented.
2. Indunil M. Hewage Washington State University
   "The population-level impact of COVID-19 vaccines: Investigating the different aspects of vaccine effectiveness."
Vaccination programs have helped reduce case numbers and the death toll of COVID-19 significantly over the past few years. The spread and control of COVID-19 have been studied by means of ODE-based compartmental models in a number of studies. However, studies on the different benefits of vaccines, other than blocking infections, remains a paucity. In this study, we developed an ODE-based compartmental model with a separate disease progression path for vaccinated individuals. Several key parameters for the vaccinated individuals were defined in terms of the respective parameters for the non-vaccinated individuals to account for the different facets of vaccine effectiveness: blocking infections; decreasing transmission; expediting recovery; reducing severe morbidity; and preventing disease mortality. Sensitivity analyses and numerical simulations on the reproduction number, infections, and disease-induced deaths provided important insights into the impact of different aspects of vaccine effectiveness on disease control. Disease burden can be reduced drastically with vaccines that have high potential in blocking infections, reducing infectivity, and speeding up recovery.
3. Tin Phan Los Alamos National Labs
   "Mathematical modeling reveals that latently infected cells reactivated by AZD5582 via the non-canonical NF-κB pathway differ substantially from productively infected cells"
AZD5582 (AZD) is a promising latency reversing agent to enable the “shock-and-kill” strategy in HIV-1 cure research, due to its potent ability to reactivate latently infected cells while maintaining high specificity by targeting the non-canonical NF-κB pathway. Previous studies in rhesus macaques have demonstrated that AZD can promote the reactivation of latently infected cells, which can lead to a viral load increase of 2-3 logs. However, the resulting reduction of the latent reservoir is less robust. Quantitative analysis of this phenomenon is difficult due to limited and fluctuating longitudinal viral load data of low amplitude. To overcome this obstacle, we developed an ensemble of mechanistic models and fit the ensemble to a combined data set from 23 macaques treated with AZD in combination with other therapies. The model ensemble recapitulates the reactivation patterns observed in SIV RNA, the change in SIV CA-DNA, and provides robust estimates of key parameters related to the reactivated cells. We find that the reactivated cells may produce fewer viruses, are less susceptible to viral cytotoxicity, and do not interact strongly with the immune response compared to productively infected cells. Reactivated cells also likely enter a temporary state that is refractory to drug effects, prior to their return to latency. These results offer practical insights on how to optimize AZD treatment.

Organized by: Tyler Cassidy (University of Leeds), Tony Humphries (McGill University)

1. Tianyu Cheng York University
   "Recurrent patterns of disease spread post the acute phase of a pandemic: insights from a coupled system of a differential equation for disease transmission and a delayed algebraic equation for behavioural adaptation"
In this talk, we propose a coupled system of disease transmission dynamics and a behavioural renewal equation to explain nonlinear oscillations post the acute phase of a pandemic. This extends the Zhang–Scarabel–Murty–Wu model, which captured multi-wave patterns during the early acute phase of the COVID-19 pandemic. Our study explores how susceptible depletion affects the coupled dynamics of disease spread and behaviour. Using risk aversion functions and delayed adaptation, we also show how these factors contribute to sustained oscillatory patterns
2. Tony Humphries McGill University
   "An immuno-epidemiological model with threshold delay"
Threshold delays arise naturally in systems with state-dependent feed-back such as those involving maturation and propagation. However, their implicit formulation and continuous state dependence present both analytical and numerical challenges. We study an immuno-epidemiological model of pathogen transmission in a large population, where the threshold delay represents a latency period that can be shortened by multiple exposures during the exposed stage. Using a heuristic linearization approach based on asymptotic expansions, we analyze the solution behavior near the steady states and compare it with that arising from two alternative formulations: a differentiated form of the threshold condition and a discrete state-dependent delay. Although both formulations leave the steady-state unchanged, they affect the local dynamics differently. Specifically, the differentiated form introduces a spurious positive eigenvalue, while the discrete state-dependent form alters the eigenvalue spectrum. To address the numerical instability induced by the differentiated form, we introduce a penalty control term that ensures the spurious eigenvalue is real and negative, hence allowing for numerical simulation. For solving boundary value problems, we demonstrate how to approximate the threshold delay by discretizing the threshold condition, which allows the use of the numerical bifurcation software package DDE-BIFTOOL.
3. Andrea Pugliese University of Trento
   "A multi-season epidemic model with random drift in immunity and transmissibility"
We consider a model for an influenza-like disease in which epidemics occur during each winter season, while the virus randomly drifts between seasons. The seasonal epidemic follow a deterministic SIR scheme (with several classes according to the year of last infection), starting with a proportion of immune individuals that depends on the fractions that were infected in the previous seasons, and on the viral drift. It is assumed that the fractions that get infected during the season are those predicted by the final size equation of structured SIR models. The viral drift is quantified (in year k) by $delta_k$, the factor reducing the immunity of all classes, and by $tau_k$, the transmissibility. The model is similar to those studied by Andreasen (2003), Roberts et al (2019) and Roberts et al (2024); however, in their models $delta$ and $tau$ are constant, while we assume that the pairs ($delta_k, tau_k$) are independent random variables with a given density q. The immunity status at the start of a season k consists of the vector (truncated to length r, meaning that all immunity is lost r years after last infection) of the population subdivided according to the number of years since last infection, and their coresponding immunity levels. We prove that the sequence of immunity status form an ergodic Markov chain that converges to a stationary distribution, that can be examined through simulations. More analytical progress is made for the case where immunity only lasts for one season (r=2): we can then explicitly compute the transition probabilities and the equations satisfied by the stationary distribution. We can also study the distribution of the effective reproduction ratio $R_E^{(k)}$, that depends on the immunity status and on the pair ($delta_k, tau_k$), and of the final attack ratio conditional on the effective reproduction ratio; this could be interesting for predicting the epidemic impact, since $R_E^{(k)}$ can be estimated at the start of a season from the exponential growth rate. Numerical computations for the case r=2 show that. for all the choices considered for the distribution of ($delta_k, tau_k$), the distribution of the attack ratio conditional on the effective reproduction ratio is very narrow.In principle, this would make it possible reliable predictions of the attack ratio knowing the effective reproduction ratio; however, estimates from influenza seasons appear in contrast with model predictions, suggesting that the model is too simple to be realistic. The model is being extended to allow for more heterogeneity, due to age structure and other factors, in the population; this should make predicted attack ratios more variable and generally lower, more in line ith empirical estimates. References Andreasen V (2003) Dynamics of annual influenza A epidemics with immuno-selection. J Math Biol 46:504–536. https://doi.org/10.1007/s00285-002-0186-2 Roberts, M.G., Hickson, R.I., McCaw, J.M. et al. A simple influenza model with complicated dynamics. J. Math. Biol. 78, 607–624 (2019). https://doi.org/10.1007/s00285-018-1285-z Roberts, M.G., Hickson, R.I. & McCaw, J.M. How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space. J. Math. Biol. 88, 48 (2024). https://doi.org/10.1007/s00285-024-02076-x
4. Tyler Cassidy University of Leeds
   "Multi-stability in an infectious disease model with waning and boosting of immunity"
The waning of immunity to an infectious pathogen can cause recurring outbreaks in a population due to the replenishment of the pool of susceptible individuals. Importantly, the dynamics of the infection at the population level is affected by the dynamics of the infectious pathogen within the individual hosts, in terms of how the infectiousness rises and falls, and how the disease-induced immunity subsequently fades. I'll discuss bistability in a simple epidemiological model that explicitly links these within-host and between-host pathogen dynamics.

Organized by: Yun Kang (Arizona State University), Tao Feng, Yangzhou University & University of Alberta

Note: this minisymposia has multiple sessions. The other sessions are: Part-2, and Part-3.

1. Gail SK Wolkowicz McMaster University
   "Analysis of a New Discrete Two-Species Competition Model"
A new discrete model of competition between two-species is introduced and analyzed. Depending upon the parameter values, the model admits all of the outcomes of the classical Lotka-Volterra like competition model: one species wins the competition independent of the initial conditions; there is a unique coexistence equilibrium that is a saddle and the winning species depends on the initial conditions; or there is a unique coexistence equilibrium that is asymptotically stable and coexistence is independent of the initial conditions. However, as well, for parameters in this model, both species can die out or there can be multiple coexistence equilibria and more than one can be locally asymptotically stable. In the symmetric case, that is all corresponding parameters are equal, unlike the classical model in which are is a line of equilibria that are all stable but not asymptotically stable, In this model there are either none, one, or three coexistence equilibria and when there are three two of the coexistence equilibria are stable and both boundary equilibria are unstable.
2. Zhisheng Shuai University of Central Florida
   "A Tale of Two Incidence Functions in Epidemiological Models"
The choice of incidence function in epidemiological modeling profoundly influences the predicted disease dynamics, especially in contexts involving population size variation and behavioral responses. In this presentation, we examine a model that incorporates post-infection mortality and partial immunity, comparing the effects of mass-action and standard incidence functions. With the mass-action incidence, the model exhibits periodic solutions under certain parameter conditions. In contrast, applying the standard incidence reduces the likelihood of periodic solutions, potentially eliminating them entirely. 
3. Qi Deng York University
   "Simulating the impact of a chlamydia vaccine in the US: An agent-based modeling approach"
Chlamydia trachomatis (CT) infection is the most reported bacterial sexually transmitted infection in the United States. Despite many cases being asymptomatic, infection can lead to complications such as pelvic inflammatory disease (PID) in females, and infertility in both females and males. We developed an agent-based transmission model to evaluate the impact of a potential CT vaccine on the prevalence of CT infections and associated PID in a population, side by side with existing screening and treatment programs. The model tracks sexually active agents aged 15-54 and simulates an evolving sexual network in a heterogeneous population consisting of heterosexuals, female sex workers and men who have sex with men. The effect of each agent’s full prior CT infection history on both CT susceptibility and, for female agents the risk of acquiring PID is modelled. The model uses a simple and flexible two-step approximate Bayesian computation (ABC) approach to calibrate both CT and PID prevalence to real-world data, allowing straightforward model adaptation to different population settings. Model “production runs” use ensembles of simulations to generate probabilistic distributions for all outputs. This model is designed to be used as a decision support tool for vaccine developers, policymakers and public health officials, able to generate actionable insights for both early-stage clinical development (to inform the selection of a vaccine performance target product profile, TPP), and for design and implementation of a CT vaccination program (to inform vaccination age, catch-up program, boosting, use of targeted versus universal vaccination, and uptake targets). It can also be used to investigate the value of re-allocating resources from screening to vaccination. We will present model results to illustrate various examples of the above use cases, using the US population as the setting. This work is supported by an NSERC grant co-funded by Sanofi.
4. Hermann J Eberl University of Guelph
   "Oscillations in a simple model of quorum sensing controlled EPS production in biofilms"
Bacterial biofilms are microbial depositions on inert surfaces. In the initial stages of biofilm formation bacteria attach to the surface, proliferate and start the production of extracellular polymeric substances that hold them together. EPS production is controlled by a quorum sensing mechanism. Biomass (cells and EPS) is detached into the aqueous environment by erosion or sloughing. Utilising the classical Wanner-Gujer 1D biofilm modeling concept one arrives at a model that consists of a system of ODEs for the reactor, a nonlocal hyperbolic system of balance laws for the biofilm proper, and a system of two point boundary value problems for dissolved susbtances such as nutrients and quorum sensing signal in the biofilm. We report and discuss numerical simulations that show the system can, depending on parameters, attain an upregulated steady state, a down-regulated steady state, and in the transition between these two passes through an oscillatory regime. This is joint work with Maryam Ghasemi and Firaz Khan.

Organized by: Meredith Greer, Prashant Kumar Srivastava, Michael Robert (Bates College), Prashant Kumar Srivastava (Indian Institute of Technology, Patna) and Michael Robert (Virginia Tech)

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Iulia Martina Bulai University of Torino, Italy
   "Modeling fast information and slow(er) disease spreading"
In the era of social networks, when information travels fast between continents, it is of paramount importance to understand how the evolution of a disease can be affected by human behavioral dynamics influenced by information diffusion. For decades, from the early 20th century, the evolution of epidemics are modelled and studied via ordinary differential equations (ODEs) systems. The compartmental models are important tools for a better understanding of infectious diseases and they have been introduce in 1927 by Kermack and McKendrick [1], in fact they can be used to predict how the disease spread, or obtain information on the duration of an epidemic, the number of infected individuals, etc., but also to identify optimal strategies for control the disease. In this work, [2], we focus on the interplay between fast information spreading and slow(er) disease spreading using techniques from Geometric Singular Perturbation Theory (GSPT). Since the pioneering papers written by N. Fenichel [3], GSPT has proven extremely suitable to describe systems evolving on multiple time scales, and analyse their transient and asymptotic behaviours. Here, we introduce an SIRS compartmental model with demography and fast information and misinformation spreading in the population. Considering the speed at which information spreads in the age of social media, we let our system evolve on two time scales, a fast one, corresponding to the information “layer” and a slow one, corresponding to the epidemic “layer”. We completely characterize the possible asymptotic behaviours of the system we propose with techniques of GSPT. In particular, we emphasise how the inclusion of (mis)information spreading can radically alter the asymptotic behaviour of the epidemic, depending on whether a non-negligible part of the population is misinformed or skeptical of misinformation. References [1] W.O. Kermack, A.G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. A115700–721 (1927). [2] I.M. Bulai, M. Sensi, S. Sottile, A geometric analysis of the SIRS compartmental model with fast information and misinformation spreading, Chaos Solitons Fractals, 185, Article 115104 (2024). [3] N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, Journal of Differential Equations, 31(1), 53-98, (1979).
2. Konstantinos Mamis University of Washington
   "Modeling correlated uncertainties in stochastic compartmental models"
In compartmental models of epidemiology, stochastic fluctuations are often considered in parameters such as contact rate to account for uncertainties originating from environmental factors, variability in human behavior patterns, and also changes in the pathogen itself. The usual choice for modeling stochastic fluctuations is white noise; however, white noise cannot incorporate the correlations arising in human social behavior. The mean reverting Ornstein–Uhlenbeck (OU) process is a more adequate model for the stochastic contact rate that includes correlations in time. The main objection to the use of white or OU noises is that they may result in contact rate taking negative values, since they are unbounded Gaussian processes. For this reason, the correlated and lognormally distributed logarithmic Ornstein-Uhlenbeck (logOU) noise has been proposed for contact rate perturbation. Furthermore, logOU noise can model the presence of superspreaders in the population because of its long distribution tail. For a stochastic Susceptibles-Infected-Susceptibles (SIS) model, we are able to analytically determine the stationary probability density of the infected, for white and Ornstein-Uhlenbeck noises. This allows us to give a complete description of the model’s asymptotic behavior and the noise-induced transitions it undergoes as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the logOU noise, where the probability density is not available in closed form, we study the noise-induced transitions using Monte Carlo simulations. This enables us to compare the model’s predictions on the severity of the disease outbreak for the different types of noise.
3. Elizabeth Amona Virginia Commonwealth University
   "Essential Workers at Risk: An Agent-Based Model with Bayesian Uncertainty Quantification"
Essential workers face elevated infection risks due to their critical roles during pandemics, and protecting them remains a significant challenge for public health planning. This study develops an Agent-Based Modeling (ABM) framework to evaluate targeted intervention strategies, explicitly capturing structured interactions across families, workplaces, and schools. We simulate key scenarios—including unrestricted movement, school closures, mobility restrictions specific to essential workers, and workforce rotation—to assess their impact on disease transmission dynamics. To enhance model robustness, we integrate Bayesian Uncertainty Quantification (UQ), systematically capturing variability in transmission rates, recovery times, and mortality estimates. Our comparative analysis demonstrates that while general mobility restrictions reduce overall transmission, a workforce rotation strategy for essential workers, when combined with quarantine enforcement, most effectively limits workplace outbreaks and secondary family infections. Unlike other interventions, this approach preserves a portion of the susceptible population, resulting in a more controlled and sustainable epidemic trajectory. These findings offer critical insights for optimizing intervention strategies that mitigate disease spread while maintaining essential societal functions.
4. Dongju Lim KAIST
   "History-dependent framework of infectious disease dynamics"
Infectious disease dynamics is inherently history-dependent; when an individual is exposed to an infectious disease affects when that individual becomes infectious. However, this inherent characteristic was disregarded in previous studies using a simple history-independent ODE model, leading to significant bias in estimating key epidemiological parameters such as reproduction numbers. In this talk, we address this bias by utilizing a model that describes the history-dependent dynamics, achieving more accurate and precise parameter estimates, solely from confirmed case data. Furthermore, we address another crucial limitation of history-dependent models; they rely heavily on accurate initial conditions. While initial conditions were estimated under unrealistic history-independent assumptions in existing studies, we discovered that this approach yields biased estimates. To address this, we introduce a new history-dependent method for estimating initial conditions based on the formula that involves time-varying likelihoods of transitioning from exposure to infectious. This method reduced error in estimating initial conditions by 55% in real-world COVID-19 data. Taken together, our results offer a framework that completely describes the history-dependent dynamics of infectious disease.

Organized by: Amy Hurford (Memorial University), Michael Li, Public Health Agency of Canada

Note: this minisymposia has multiple sessions. The other sessions are: Part-2, Part-3, and Part-4.

1. Michael WZ Li Public Health Agency of Canada
   "Modeling and Prospects to Support Small Jurisdiction Public Health in Canada"
Mathematical modeling has been critical in supporting public health initiatives, providing valuable insights into disease dynamics, intervention strategies, and resource allocation. Many regional heterogeneity effects and challenges from small jurisdictions and communities were masked by the larger jurisdictions during the pandemic, however, risk exist in both directions and in many forms. In this talk, I will discuss prospects working towards supporting small-jurisdiction public health, in particular, the challenges with awareness, communication, uncertainty of information and feedbacks.
2. Wendy Xie National Collaborating Centre for Infectious Diseases
   "Lessons learned from the In the Equation Workshop: Towards Indigenous-led infectious disease modelling"
The In the Equation Workshop was held February 18-19, 2025 with the goal of initiating discussions towards Indigenous-led infectious disease modelling. Over the course of 1.5 days, presentations from the Chiefs of Ontario, First Nations Health and Social Secretariat of Manitoba, First Nations Information Governance Centre, and Inuit Tapiriit Kanatami highlighted ongoing work to advance data sovereignty and capacity building for First Nations and Inuit health research and programming. Participants engaged in facilitated discussions focused on what community-based infectious disease research means for First Nations, Métis, and Inuit communities, and how mathematical modellers can better support Indigenous-led health research. The knowledge shared at this workshop underscores the need for formal training in Two-Eyed Seeing approaches in infectious disease research and emphasizes the importance of continued relationship building among First Nations, Métis, and Inuit community leaders and modelling researchers.
3. James Watmough University of New Brunswick
   "Predicting population level immune landscapes in small communities."
Roughly speaking, outbreaks of respiratory infectious, such as measles, CoViD-19, and influenza, are shaped by two main factors: (1) the patterns and nature of contacts between individual hosts, and (2) the distribution of immunity locally and regionally within the host population. The strength and duration of an individual host's immune response depends on individual traits and the characteristics of exposure, which are at least partially dependant on the nature of contacts between hosts. Thus, the dynamics of disease spread and waning immunity at the host-population level are driven by a fixed landscape of immune-traits based on demographics, comorbidities, and other individual factors affecting disease severity, and a dynamic immune landscape shaped by prior outbreaks. Contact patterns between hosts reflect community structure and the relative strengths of within group and between group contacts. This contact structure can be very different for smaller isolated communities and small communities nestled in larger metropolises. The main objective of this talk is to present preliminary results from simple compartmental and individual-based models designed to predict population-level distributions of disease burden and immunity from host community structure and within-host virus and immune dynamics. Of particular interest is the role of community structure in determining the size and severity of outbreaks in smaller jurisdictions.
4. Abdou Fofana and Amy Hurford Memorial University
   "Fitting and counterfactual scenarios for epidemiological data describing intermittent periods of travel-related cases and community spread"
When infectious disease dynamics are dominated by community spread there are established methods to estimate the transmission rate for an epidemic compartment model and for how to do counterfactual scenarios. But how should this same analysis be done if infectious disease spread occurs as intermittent periods of travel-related cases and community outbreaks? In this talk, we will describe the importation-community spread switch model. This model considers data describing infections that arise from contact with an infectious person in another community (travel-related cases) or with an infectious person in the local community (community cases). The importation-community spread switch model includes a spillover model that describes the probability that a travel-related case initiates a community outbreak. We fit the importation-community spread switch model to COVID-19 data from the Canadian province of Newfoundland and Labrador. We describe how the estimated parameters are used in a counterfactual simulation framework. Canada consists of large jurisdictions and small jurisdictions, such as Newfoundland and Labrador. The importation-community spread switch model generalizes fitting and simulation approaches so that they can be applied to a broader range of Canadian jurisdictions.

Organized by: Abba Gumel (University of Maryland), Alex Safsten, Arnaja Mitra (both University of Maryland)

Note: this minisymposia has multiple sessions. The other sessions are: Part-2, and Part-3.

1. Michael Robert Virginia Tech
   "Climate-informed mitigation of mosquito-borne disease: the case of dengue in an emerging environment"
Mosquito-borne diseases endemic to areas with tropical climates have been spreading in temperate regions of the world with greater frequency in recent years. Numerous factors contribute to this spread, including urbanization, increases in global travel, and changes in temperature, precipitation, and humidity patterns due to climate change. Understanding the role of climate in mosquito-borne disease emergence and spread is critical for projecting future outbreaks and informing control measures. We have developed mathematical models incorporating temperature and precipitation into mosquito population and disease transmission dynamics to investigate how seasonal fluctuations in meteorological variables impact the probability and magnitude of outbreaks. We have parameterized these models for recent dengue outbreaks in the temperate city of Córdoba, Argentina, and with these models, we investigate strategies for implementing different mosquito control measures. By incorporating projections for future climate scenarios, we also investigate how approaches to control may need to change as temperatures increase and precipitation patterns become more erratic as a result of climate change.
2. Salihu Musa University of Maryland
   "Mathematical modeling of the geo-spatial dynamics of Lyme disease under various climate change projection scenarios"
Lyme disease, the most common vector-borne disease in North America, is increasingly prevalent in Maryland, with climate change, particularly rising temperatures, accelerating its spread. Temperature plays a critical role in the ecology of Ixodes scapularis ticks and the transmission dynamics of Borrelia burgdorferi, affecting both vector-host interactions and the seasonal timing of disease risk. In this study, we develop a temperature-driven epidemiological model to investigate the spatial and temporal spread of Lyme disease across Maryland. By integrating ecological and climate datasets with temperature- dependent tick-host interactions, we assess how warming patterns influence tick proliferation, seasonal activity, and disease transmission intensity. Simulations under Representative Concentration Pathways (RCP 4.5 and 8.5) project substantial increases in disease burden, with particularly pronounced effects in Central and Western Maryland. We further evaluate the impact of vector control strategies and show that combining habitat modification with rodent-targeted interventions significantly reduces the basic reproduction number (Ro), especially when community participation in environmental clearance exceeds 50%. Spatial projections also indicate a northward shift in high-risk zones, highlighting the evolving geographic landscape of Lyme disease risk. This work provides a quantitative framework for optimizing prevention strategies and informing climate-resilient public health policies aimed at mitigating Lyme disease transmission in a warming environment.
3. Kathleen Hoffman University of Maryland Baltimore County
   "Parameter Sensitivity, Identifiability, & Estimation for a Data-Driven Model of Malaria"
Parameters are ubiquitous in biological models and significantly influence the model behavior. While some parameters can be estimated from experimental data, many cannot . This work focuses on the role of parameters in two vector-borne diseases: malaria and dengue fever. Parameter identifiability considers the mapping of parameters to observables with and without noise. We compute the Sobol index to determine the sensitivity of the parameters, that is how the output changes in response to changes in the parameter values. Finally, we use techniques from data assimilation for forward prediction and to estimate parameters that cannot be determined from experimental data alone. Joint work with Mac Luu, Katie Gurski, Animikh Biswas, Nigel Seymour, Owen McMann
4. Abba Gumel University of Maryland
   "Recent advances and challenges in the mathematics of malaria dynamics"
Since its spillover to humans some 12,000 years ago, malaria, a deadly parasitic disease transmitted between humans via the bite of an infected adult female Anopheles mosquitoes, remains one of the deadliest infectious diseases of mankind. Much progress has been recorded in the battle against malaria over the last decade or two, prompting a renewed quest to significantly reduce its burden (by 90% by 2030) or eradicate it by 2040. Unfortunately, these efforts are threatened by several challenges, such as widespread resistance to all the currently-available insecticides used in vector control, evolution of drug resistance, climate change, land-use changes, emergence of invasive species, human mobility (rural-urban migration), and quality of public health infrastructure and care. I will discuss some of these advances and challenges associated with the mathematical modeling and analysis of malaria transmission dynamics, aimed at assessing the impacts of some of the aforementioned factors that potentially get in the way of the malaria eradication objective.

Organized by: Yun Kang (Arizona State University), Tao Feng, Yangzhou University & University of Alberta

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-3.

1. Yaqi Chen Harbin Institute of Technology & University of Alberta
   "Well-Posedness and Dynamical Behavior of a Two-Species Reaction-Diffusion Model with Nonlocal Perception"
Nonlocal cues, such as visual, auditory, olfactory, and chemosensory cues, play a vital role in informing animal movement. To characterize these ecological phenomena, we propose a two-species reaction-diffusion model with nonlocal perception in a two-dimensional square domain. In this talk, I will first discuss the well-posedness of the proposed model, which is established using the entropy method. Subsequently, taking the predator-prey system as an illustrative example, I will conduct linear stability and bifurcation analyses by selecting the perception diffusion coefficient as a bifurcation parameter. The conditions for stability of positive constant steady states, as well as for the existence of Turing instability and Turing-Hopf bifurcations, will be identified explicitly. Furthermore, numerical simulations of the predator-prey model with a Holling type II functional response will be presented, including spatially nonhomogeneous steady-state patterns and spatially nonhomogeneous periodic patterns. These results highlight a complementary mechanism between perceptual range and  perception diffusion ability, offering new theoretical insights and quantitative understanding of the role of nonlocal perception in spatial self-organization and pattern formation in ecological systems. This is joint work with Ben Niu and Hao Wang.
2. Shan Gao University of Alberta
   "Early detection of disease outbreaks and non-outbreaks using incidence data: A framework using feature-based time series classification and machine learning"
Forecasting the occurrence and absence of novel disease outbreaks is essential for disease management, yet existing methods are often context-specific, require a long preparation time, and non-outbreak prediction remains understudied. To address this gap, we propose a novel framework using a feature-based time series classification (TSC) method to forecast outbreaks and non-outbreaks. We tested our methods on synthetic data from a Susceptible–Infected–Recovered (SIR) model for slowly changing, noisy disease dynamics. Outbreak sequences give a transcritical bifurcation within a specified future time window, whereas non-outbreak (null bifurcation) sequences do not. We identified incipient differences, reflected in 22 statistical features and 5 early warning signal indicators, in time series of infectives leading to future outbreaks and non-outbreaks. Classifier performance, given by the area under the receiver-operating curve (AUC), ranged from 0.99 for large expanding windows of training data to 0.7 for small rolling windows. The framework is further evaluated on four empirical datasets: COVID-19 incidence data from Singapore, 18 other countries, and Edmonton, Canada, as well as SARS data from Hong Kong, with two classifiers exhibiting consistently high accuracy. Our results highlight detectable statistical features distinguishing outbreak and non-outbreak sequences well before potential occurrence, in both synthetic and real-world datasets presented in this study.
3. Bo-Wei Qin Fudan University
   "Polarization Does Not Necessarily Imply Conflict: Modeling and Modulating Pattern Boundaries of Opinion Dynamics"
Divergent opinions resulting from polarization are widespread across various fields, including economics, technology, and politics, and are often considered as social threats. Numerous studies were therefore devoted to achieving consensus. However, as we will discuss in this talk, polarization is inevitable when individuals exhibit black-and-white thinking (BWT), a previously underappreciated mechanism that drives adaptive consolidation of opinions. We will also demonstrate that the primary social threats do not arise directly from polarization itself, but rather from conflicts between connected individuals holding divergent opinions. By developing a networked dynamical model incorporating BWT and analyzing the pattern boundaries, we find that polarization does not necessarily imply conflict. Instead, the conflict intensifies through accumulating unstable eigenmodes, a process that is greatly influenced by network topology. This finding helps us elucidate how conflicts evolve across different social networks, and, more importantly, provides insights into developing effective modulation strategies to mitigate conflicts, even when polarization persists.
4. Joan Ponce Arizona State University
   "Extreme geographic misalignment of healthcare resources and HIV treatment deserts in Malawi"
The Joint United Nations Programme on HIV and AIDS has proposed that human rights should be at the center of efforts to end the HIV pandemic and achieving equity in access to antiretroviral therapy (ART) and HIV healthcare is essential. Here we present a geospatial and geostatistical modeling framework for conducting, at the national level, an equity evaluation of access to ART. We apply our framework to Malawi, where HIV prevalence is ~9%. Access depends upon the number of available healthcare facilities (HCFs), the travel times needed to reach these HCFs, the mode of transportation used (walking, biking, driving) and the supply-to-demand ratio for ART at the HCFs. We find extreme inequities in access to ART. Access maps show striking geographic patterns, revealing clusters of communities with very low or high levels of access. We discover that an extreme geographic misalignment of healthcare resources with respect to need has generated a new type of medical desert: an HIV treatment desert. Around 23% of people living with HIV reside in deserts where they have to walk up to 3 h to reach HCFs; in 2020, these HCFs only received 3% of the national supply of ART. We recommend strategies for shrinking deserts; if not implemented, deserts will grow in size and number.

Organized by: Amy Hurford (Memorial University), Michael Li, Public Health Agency of Canada

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-2, and Part-3.

1. Reilly Comper Trent University
   "A meta-population disease model for the transmission of highly pathogenic avian influenza H5N1 within and between dairy herds in Ontario, Canada to assess the potential risk of pathogen spillover to dairy workers"
Introduction: Since first being identified in March 2024, the outbreak of highly pathogenic avian influenza H5N1 (HPAI-H5N1) in United States (US) dairy cattle has affected 973 herds across 17 states. The outbreak among cattle has subsequently led to 41 confirmed spillover cases in humans with a known exposure to infected dairy cattle. Canadian cattle remain unaffected by the HPAI-H5N1 outbreak. Preparedness and preparation during this time is critical and may help to mitigate the size and duration of such an outbreak should introduction of HPAI- H5N1occur in Canada. Objectives: The objectives of this study were to construct a meta-population disease model of HPAI-H5N1 in Ontario dairy cattle, parameterized based on empirical dairy cow movement networks, and to assess the potential for spillover infections to occur within Ontario dairy farm workers. Methods: The meta-population model was built using the ‘SimInf’ package in R. The within-herd disease model was constructed using a stochastic SIR model framework and the system of between-herd dairy cow movements was based on random networks parameterized using historical Ontario dairy cow network data. Introduction of HPAI-H5N1 was assumed to occur through importation of infected cattle from the United States, the number and regional distribution of which were also based on historical data. A human spillover function was parameterized using data from the 2024 HPAI-H5N1 dairy outbreak in California, and the spillover function was applied to the results of the meta-population model simulations to estimate the number of projected dairy cow-to-human spillover events in Ontario. Ten thousand model simulations were run for one year and the number of primary herd infections (infected through importing infectious dairy cattle), secondary herd infections (infected through the domestic movements of an infectious dairy cow(s) between Ontario herds), and human spillover cases were quantified. Results: Simulations of the meta-population model resulted in the majority of infected herds being those that imported infectious dairy cows (IQR: 12-16; range: 4-26). Due to the highly fragmented network of domestic between-herd dairy cow movements in Ontario, the number of secondary infection herds (i.e., Ontario herds receiving an infectious cow from another Ontario herd) ranged from 0-5, with approximately 56% of model iterations resulting in no between-herd transmission of HPAI-H5N1 within Ontario. Spillover of HPAI-H5N1 to human farm workers was very rare, occurring in only 8/10,000 model iterations with no more than a single spillover event per iteration.
2. Clotilde Djuikem University of Manitoba
   "Threshold-based impulsive biocontrol for coffee leaf rust"
Coffee leaf rust (CLR) severely affects coffee production worldwide, leading to reduced yields and economic losses. To reduce the cost of control, small-scale farmers often only apply control measures once a noticeable level of infection is reached. In this work, we develop mathematical models to better understand CLR dynamics and impulsive biocontrol with threshold-based interventions. We first use ordinary and impulsive differential equations to describe disease spread and the application of control measures once a certain infection level is detected. These models help determine when and how often interventions should occur. To capture the early stages of the disease and the chance that it might die out by itself, we then use a continuous-time Markov chain approach. This stochastic model allows us to estimate the probability that the pathogen fails to establish, thereby avoiding serious outbreaks.
3. Sayeda Irin Akter York University
   " Modeling the Effect of Social Distancing on the Spread and Control of Infectious Diseases Using Point Pattern Process"
This work explores the spatial dynamics of disease transmission using Point Pattern Processes (PPPs) and distance-dependent infection rate within a Susceptible-Infectious-Removed-Susceptible (SIRS) framework. By modeling individuals as points in a continuous space, we examine how social distancing and spatial separation influence the spread of the virus. The infection rate is not uniform but varies with the distance between individuals, simulating the real-world effects of reduced contact through interventions like social distancing. We use mathematical models and point pattern analysis to investigate different spatial configurations, from clustered (high transmission risk) to dispersed (reflecting effective social distancing). The pair correlation function g(r) is employed to capture spatial clustering, while pair approximation simplifies the modeling of spatial interactions by considering the effect of pairwise interactions. Prior to social distancing, high $P_I$ probability of infection values are observed due to frequent close contacts, leading to clustered transmission patterns. After implementing social distancing, $P_I$ decreases as individuals are more dispersed, reducing the likelihood of infection. This approach allows us to quantify the impact of public health measures on transmission dynamics, providing insights for optimizing interventions to control the spread of disease.
4. Rachael Milwid PHAC
   "Making something from nothing: Using a spatially explicit modelling approach to study Arctic fox rabies in a data-poor environment"
The Canadian Arctic is vast, sparsely populated, extreme in climate, and home to Arctic fox rabies. Field data collection on Arctic foxes and rabies therefore faces many obstacles despite the persistent threat of rabies to many northern communities. Here, we addressed the challenge of data scarcity in the Arctic rabies system by using a spatially explicit agent-based modelling (ABM) approach. Specifically, we simulated both Arctic fox (Vulpes lagopus) and encroaching red fox (Vulpes vulpes) populations on a broad geographic area centered around Churchill, Manitoba. We then introduced rabies into Arctic foxes at varying prevalences within the Churchill area and simulated the model for 50 years. Biological and epidemiological input parameters were informed by existing empirical data from the literature, while unknown parameters (e.g., transmission rates between Arctic and red foxes) were tested across their entire parameter space. This modelling approach allowed us to 1) narrow certain biological and disease parameter spaces where field study values are lacking, and 2) assess the influence of these parameters on rabies persistence and other disease dynamics in northern Manitoba. The findings of our study provide an insight into the effects of the northward expansion of the red fox and its effect on the Arctic rabies system. The ABM and resulting parameter sets will be used as a basis to simulate rabies transmission in the Canadian Arctic and to assess the effectiveness of rabies control strategies aimed at protecting public health in Churchill, Manitoba.

Organized by: Iain Moyles (York University), Rebecca Tyson, University of British Columbia Okanagan

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Sarah Machado-Marques York University
   "Considering the effects of pair formation dynamics on mpox and HIV co-infection in the gbMSM community"
There is a growing need to explicitly consider how behaviour plays a role in the spread of diseases transmitted through close, prolonged contact. In particular, the duration individuals spend single or in relationships has yet to be incorporated into co-infection models, potentially underestimating the protective effects of stable partnerships. We propose an mpox and HIV co-infection model that explicitly incorporates the formation of pairs between individuals. We demonstrate that considering pair formation and dissolution rates are critical in determining outbreak potential and severity. These considerations remain important beyond the initial stages of the outbreak and can lead to more accurate predictions. Our work highlights that the particular pairing context and serological status of the population should always be carefully considered prior to intervention on behavioural patterns.
2. Bridgette Amoako University of Guelph
   "Sexual Behaviour and Mpox Transmission in an Agent Based Model"
We present an agent-based framework that uses a dynamic signaling game to model mpox transmission in a population of gay and bisexual men who have sex with men (gbMSM). The model focuses on how agents' beliefs about a partner’s infection status influence their decisions to pursue or abstain from casual sexual encounters. Agents are subject to mpox’s typical incubation and infectious periods and become immune upon recovery. Immunity could also be obtained through vaccination. Within this framework, each agent updates their risk perception based on both individual encounters and broader disease prevalence, then selects a strategic response to potential partners. By examining how risk perception interacts with behavior, as well as how the timing and efficacy of vaccination factor into disease spread, we aim to provide insights into which conditions are most conducive to large outbreaks or successful containment. This approach highlights the role of dynamic, feedback-driven behaviors in shaping the course of mpox epidemics and can help inform strategies for more effective vaccination and public health interventions.
3. Pouria Ramazi Brock University
   "Enough but Not Too Many: Modeling and Dynamics of Bi-Threshold Social Behavior"
This work introduces and analyzes bi-threshold models of social behavior, where individuals adopt actions only when their prevalence lies between a personal lower and upper threshold. This captures real-world dynamics like fashion trends or information spread, where behaviors are appealing when moderately common but lose appeal if too rare or too widespread. Theoretical results show that while small populations may exhibit persistent fluctuations, these fade as population size increases, with dynamics converging to equilibrium. Empirical validation on social media data confirms the model’s superior predictive power over traditional threshold models, particularly in capturing phases of behavioral decline.
4. Clark KendrickGo Ateneo de Manila University
   "Exploring Mathematical Techniques in Collective Behaviour and Decision Making in Animal Groups"
Collective behaviour in animal groups are coordinated movements and interactions among members that aim to achieve a common goal. Whether these goals are for allocation of resources or defence from predators, the collective behaviour appears to be largely a group activity initiated by a member, known as the leader. In the absence of high-resolution spatio-temporal data, various qualitative studies offer a glimpse of how leader-follower interactions take place. For example, Nagy, et al., studied the average delay in response when pigeons change the direction inflight. Next, Bourjade, et al., studied the first mover and the succeeding order of movements of Przewalski's Horses. Furthermore, various studies on the collective motion in the animal kingdom offer mathematical models and infer how the interactions and decision making take place. Important questions arise during an event of coordinated motion in animals. During such an event, do individuals move according to a certain set of natural rules? Or certain patterns form due to the influence of a leader? How is this influence measured? Finally, how is influence transferred to other members of the group? In this study, we discuss the role of information theory to quantitatively uncover leader-follower relationship in a horse group. Specifically, we introduce concepts from information theory, specifically global and local transfer entropy being applied to a harem of horses. We will discuss their definitions, and how these key concepts are used to support causation in events. We will then discuss some important implications on how this technique can be used to analyse collective motion where data is scarce.

Organized by: Abba Gumel (University of Maryland), Alex Safsten, Arnaja Mitra (both University of Maryland)

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-3.

1. Katharine Gurski Howard University
   "Building a Model for Seasonal Malaria Chemoprevention and Drug Resistance"
Seasonal malaria chemoprevention has been shown to cut clinical malaria episodes by up to 75% in high-risk areas. However, when chemoprevention is given in an area with drug-resistant parasites, there is a risk of the long-term growth of drug-resistance outweighing the benefits of the immediate reduction in deaths of children. We aim to study this situation with data driven pharmacokinetics and pharmacodynamics, experimental data on gametocyte growth within an infected human, gametocyte decay within a treated human, and the probabilities of infecting a mosquito who bites either an infected or treated human by modeling gametocyte transmission. We formulate a model by considering arbitrarily distributed sojourn for various disease stages and chemoprevention. We consider the lessened effectiveness of treatment on drug-resistant parasites. With the use of gamma distributions fit to data, the system can be reduced to a system of ODEs, with non-trivial characteristics which are only captured by non-exponential distributions for disease stages and susceptibility.
2. Yves Dumont French Agricultural Research Centre for International Development
   "Reducing nuisances or minimizing epidemiological risks: which is the best choice with the Sterile Insect Technique?"
The sterile Insect Technique (SIT) is a promising biological control method against vectors of human diseases, like mosquitoes. SIT can be used either to reduce the nuisance (mosquito bites), or to reduce the epidemiological risk. Depending on the objective, the releases strategy is not the same. Since SIT is an autocidal method, it takes time to notice any effect. Reducing nuisances requires a significant reduction in the wild mosquito population. This generally requires mass releases and, consequently, the production of large numbers of sterile mosquitoes, and, time. When SIT is used to reduce the epidemiological risk, it is preferable to release sterile males only because sterile females may transmit viruses during blood meal on humans. Even if sexing methods have become increasingly efficient, allowing males to be separated from females, it is important to estimate the maximum number of sterile females per release, without, however, increasing the epidemiological risk. In this presentation, I will present some theoretical results and illustrate some of them with numerical simulations in order to discuss the best strategies depending on whether we want to reduce the nuisance, or the epidemiological risk, with SIT.
3. Alex Safsten University of Maryland
   "Leveraging inter-species competition to improve the effectiveness of the sterile insect technique"
Mosquitos top the list of the deadliest animals in the world due to the diseases they carry and transmit to humans, including malaria, West Nile virus, and dengue, with malaria being the most important vector-borne disease of mankind. Existing methods of mosquito control heavily rely on using chemical insecticides to kill them. Unfortunately, however, in the context of malaria for instance, the heavy and widespread use of these insecticides in endemic areas has resulted in widespread resistance to all the chemical compounds currently used in vector control. This necessitates the use of alternative methods for vector control. The sterile insect technique (SIT), which entails the periodic mass release of sterilized male mosquitoes into an environment where adult female mosquitoes are abundant, is one of the main promising approaches being proposed. The eggs laid by females that mated with sterile male mosquitoes will not hatch, thereby potentially reducing the population of the wild mosquitoes in the environment. I will present an ODE model of SIT and several strategies eliminating disease-carrying mosquitoes including using optimal and feedback control for adjusting the rate of release of sterile males as the wild population is reduced and leveraging interspecies competition from less-harmful species. I will also present a PDE model of SIT which demonstrates the spatio-temporal dynamics of SIT and allows for the development of strategies for, e.g., inducing counter invasions of non-disease-carrying mosquitoes that have recently been pushed out of their historical ranges by their disease-carrying cousins.
4. Zhuolin Qu University of Texas San Antonio
   "Multistage spatial model for informing release of Wolbachia-infected mosquitoes as disease control"
Malaria remains one of the leading causes of infectious disease mortality worldwide, disproportionately affecting young children and vulnerable populations. Its transmission is shaped by complex interactions between host immunity, vector dynamics, and environmental seasonality. In this talk, I will introduce a mathematical modeling framework that captures age-structured malaria transmission in both year-round and highly seasonal settings. The model integrates the development of immunity through repeated exposure and accounts for the nonlinear feedback between immunity and disease spread. I will discuss how we use this framework to explore the timing and design of vaccination strategies, particularly in environments with strong seasonal variation. Along the way, I’ll highlight key modeling challenges, share insights from our sensitivity analysis, and reflect on how mathematical tools can inform more effective and context-specific malaria control interventions.

Organized by: Yun Kang (Arizona State University), Tao Feng, Yangzhou University & University of Alberta

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-2.

1. Matthew Wheeler University of Florida
   "Linking Network Architecture to Dynamic Behavior"
Modularity is a key feature of biological systems that is well accepted and studied in biology. However, from a mathematical standpoint, it remains poorly defined. In previous work, we developed a decomposition theory based on feedback loops, linking network structure to the organization of its dynamics. We went on to propose that an appropriate definition for a module of a network are the irreducible objects of this decomposition theory.  In this talk, we present a categorical framework for dynamical systems that significantly broadens the scope of our original approach. This generalization extends the decomposition theory to a wider class of systems, providing deeper insight into the structure-dynamics relationship and offering powerful new tools for analyzing complex biological networks.
2. Xingfu Zou University of Western Ontario
   "Infection forces mediated by behaviour changes with demonstration by a DDE  model"
In this talk, we will revisit the notion of infection force from a new angle which can offer a new perspective to motivate and justify some infection force functions. Our approach not only can explain  many existing infection force functions in the literature, it can also motivate new forms of infection force functions, particularly infection forces depending on disease surveillance of the past. As a demonstration, we propose an SIRS model with delay. We comprehensively investigate the disease dynamics represented by this model, particularly focusing on the local bifurcation caused by the delay and another parameter that reflects the weight of the past epidemics in the infection force.  We confirm Hopf bifurcations both theoretically and numerically. The results show that depending on how recent the disease surveillance data are, their assigned weight may have a different impact on disease control measures.
3. Daniel B. Reeves Fred Hutchinson Cancer Center
   "Modeling HIV reservoir ecology and selection through the lens of CD4+ T cell kinetics"
The latent reservoir of HIV persists for decades in people living with HIV (PWH) on antiretroviral therapy (ART). To determine if persistence arises simply from natural behaviors of CD4+ T cells harboring HIV proviruses, we use ecological models to contrast the clonal dynamics of HIV vs memory CD4+ T cell sequences from the same PWH. We show HIV reservoirs are more clonal than general CD4+ T cells and that increasing reservoir clonality over time with decay of intact proviruses cannot be explained by CD4+ T cell kinetics alone. We develop a stochastic multitype branching process model that describes the dynamics of CD4+ T cells, some of which harbor HIV proviruses. We test nearly 1000 combinations of model mechanisms against a broad range of experimental observations, finding that weak selection against intact proviruses (s~0.06) is a parsimonious explanation for all data. These results help to understand the long-term dynamics of HIV reservoirs in PWH on ART and may inform immunotherapies for HIV cure.
4. Gregoire Ranson York University
   "Qualitative impact of political and economic decisions on PrEP users under HIV epidemic control"
In this work, we explore the dynamics of a hybrid differential–difference system with delay describing an HIV SI-model with protected compartment (PrEP) described by an age-structured equation and nonmonotonic recruitment rate. The limited protection duration offered induces a delay in the system. First, we study the existence of equilibria. Under our assumption, we show that the system exhibits several steady states without infection, which challenges the study. After a local stability analysis of each equilibrium, we study the existence of a Hopf bifurcation around the endemic equilibrium. Our results show that the delay may destabilize the endemic steady state and lead to the existence of recurrent periodic epidemic waves. Each situation is illustrated by numerical simulations.

Organized by: Nir Gavish (Technion)

1. Nir Gavish Technion Israel Institute of Technology
   "Optimal vaccination for contagious diseases with seasonal transmission"
We consider epidemiological models with seasonality and ask what the optimal temporal vaccination profile is that minimizes the basic reproduction number defined over a season, given a constraint on the total annual number of vaccinations. We do not impose any a priori assumptions about the structure or regularity of the optimal vaccination profile. In particular, we allow the vaccination profile to include delta functions corresponding to pulse vaccination. To do so, we consider a periodic optimal control problem over a measure space. Using non-standard tools that do not rely on Pontryagin's theorem for optimal control problems, we characterize the solution to the problem. In addition, we develop an efficient numerical scheme for computing the optimal vaccination profile over time. This is a joint work with Guy Katriel
2. Amit Huppert Tel Aviv University
   "Modeling Predation in Bacterial Interactions"
We developed a mathematical model to explore density-dependent predation in microbial systems. Density dependence is a fundamental ecological mechanism that influences population dynamics and regulation. While mathematical modeling is a valuable tool for quantifying predator-prey interactions, a research gap exists in exploring the nature of predator growth's dependence on prey density through a combination of empirical and mathematical approaches within the prey-predator framework. We developed mathematical ODE models and fitted them to experimental time-series data from microbial predator-prey systems. These models incorporated different functional responses—specifically Holling types I, II, and III—which describe the relationship between prey density and predator foraging. Parameter inference was performed using a Bayesian approach with the Markov Chain Monte Carlo (MCMC) technique, adapting the framework to handle multi-replicate time-series data. We employed two distinct modeling approaches: Single Interval Modeling, which fits one model to the entire dataset, and Phased Interval Modeling, which divides the 96-hour period into three distinct phases (0-12, 12-48, and 48-96 hours) and fits separate models to each. Model selection in both approaches was based on likelihoods, AIC, and BIC. The study revealed distinct dynamics in each phase. In Phase I, the predator's per-capita growth rate (PGR) was density independent, and a simple model assuming the predator's total time was spent handling prey provided a good fit with an analytical solution. Phase II exhibited density-dependent dynamics, where the predator's PGR changed with prey density; the best model for this phase was an ODE model with a Holling type-III functional response. In Phase III, following prey depletion, the predator population showed exponential death, and its PGR was again density independent.
3. Byul Nim Kim Kyung Hee University
   "Empirical and Spatiotemporal Approaches to Effective Reproduction Number Estimation: Insights from Network and Mobility Models in South Korea"
Understanding the effective reproduction number (R_t) is crucial for real-time epidemic assessment and public health intervention. This presentation introduces and synthesizes three advanced approaches for estimating Rt during the COVID-19 pandemic in South Korea, highlighting their methodological innovations and practical implications. First, the Transmission Potential (TP) model integrates household vs. non-household transmission, mobility patterns (via Google data), and social distancing behaviors to estimate Reff in real time. By distinguishing the impact of mobility changes on different transmission settings, this model provides dynamic and context-aware Reff estimates, outperforming conventional methods like Cori's Rt in sensitivity and short-term prediction​. Second, an empirical infection network-based R_t model uses real-world infector-infectee pair data to directly compute R_t without relying on assumptions of homogeneous mixing. This network approach captures the heterogeneity of regional and demographic transmission, especially during superspreading events and early epidemic phases, where traditional models often underperform​. Third, a multi-patch SEIIR model with mobility-informed regional Reff quantifies both local and interregional transmission. Using high-resolution mobility data and compartmental modeling across 17 regions, it reveals Seoul and Gyeonggi as dominant transmission hubs. The study emphasizes phase-specific and region-targeted mobility interventions as more effective than uniform national policies​. Together, these studies highlight the need for adaptive, data-driven R_t estimation frameworks that incorporate real-time behavior, mobility, and infection network structures. The integration of these methods advances epidemic modeling and supports refined public health strategies tailored to regional and temporal dynamics.
4. Kyeongah Nah National Institute for Mathematical Sciences
   "Age-structured modeling of tuberculosis in South Korea and insights for national control strategies"
Despite improvements in its national tuberculosis (TB) control program and rapid economic growth, South Korea continues to report the highest TB incidence among OECD countries. Addressing this challenge requires an understanding of the changing trends of TB burden across different age groups and a long-term evaluation of policies aimed at TB control. This study introduces an age-structured population dynamics to analyze the dynamics of TB transmission under national control in Korea. We perform retrospective assessments and future projections to assess the impact of Public-Private Mix (PPM) strategies on TB incidence. Additionally, we explore how this model could be extended to provide insights for designing effective TB control policies.

Organized by: Abba Gumel (University of Maryland), Alex Safsten, Alice Oveson (both University of Maryland)

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-3.

1. Mallory Harris University of Maryland
   "Risk (Mis)estimation and Population Heterogeneity Shape Infectious Disease Dynamics"
Models of human behaviour during infectious disease outbreaks often assume that people perfectly assess the risks associated with infection and become more cautious when risk is high. However, prior work showed that people tended to misestimate the risk of Covid-19 exposure at events of different sizes (Sinclair et al 2021, PNAS). The effects of event risk estimation have not been studied at population level, a critical gap given potential for nonlinear and emergent dynamics in infectious disease systems. Here, we build an agent-based model to capture feedback between infectious disease dynamics, risk perception, and behavior in the context of event attendance. At each time step, individuals decide whether to attend an event based on their assessed exposure risk, a function of event size and prevalence calibrated to actual risk assessments collected from 11,169 individuals across the United States between September 2021 and August 2022 (Sinclair et al 2023, PLoS One). We show that risk misestimation substantially worsens epidemic burden compared to what it would be if people estimated risk perfectly. Behavioural interventions to improve risk estimation reduce but do not completely eliminate this effect. We also compare strategies for deploying behavioural interventions across a heterogeneous population where certain subgroups are more likely to underestimate risk. This work underscores the importance of considering risk misestimation in mathematical models of infectious diseases and demonstrates benefits of behavioural interventions to improve individual decision-making and reduce disease transmission. Joint work with Shu Yuan Shi and Joshua Weitz.
2. Christian Parkinson Michigan State University
   "Optimal Control of a Reaction-Diffusion Epidemic Model with Noncompliance"
We consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a portion of the population does not comply with them, and this noncompliance affects the spread of the disease. Drawing from social contagion theory, our model allows for the spread of noncompliance parallel to the spread of the disease. Control variables affect the infection rate among the compliant population, the rate of spread of noncompliance, and the rate at which non-compliant individuals return to a compliant state. We prove the existence of global-in-time solutions for fixed controls and study the regularity properties of the resulting control-to-state map. We establish the existence of optimal controls for a fairly general class of objective functions and present a first-order stationary system which is necessary for optimality. Finally, we present simulations with various parameters values to demonstrate the behavior of the model.
3. Zitao He University of Waterloo
   "From Sentiment to Spread: Homophily and Early Warnings in Epidemic Dynamics"
Understanding the interplay between social activities and disease dynamics is crucial for effective public health interventions. While many coupled behavior-disease models assume homogeneous populations, real-world social structure is often heterogeneous. In this talk, we present a model that divides the population into social media users and non-users to investigate the impact of homophily (the tendency for individuals to associate with similar others) and online events on disease dynamics. We find that homophily slows down the spread of vaccinating strategies, pushing the system closer to a tipping point where vaccine uptake collapses and an endemic equilibrium emerges. Online events also play an important role, with early social media discussions acting as warning signs of upcoming outbreaks. Building on these insights, we also discuss a data-driven approach that uses deep learning to detect early warning signals from vaccine-related social media time series. Specifically, we train LSTM and ResNet classifiers on simulated data from a stochastic behavior-disease model with additive Lévy noise, capturing heavy-tailed real-world fluctuations. These classifiers consistently outperform conventional indicators such as variance and lag-1 autocorrelation, offering clearer and more interpretable signals. Together, these studies underscore the importance of incorporating social structure and real-time data in predictive models for proactive public health response.
4. Alice Oveson University of Maryland
   "Modeling Racial and Age-Structured Transmission Dynamics with Empirical Contact Data"
I present a compartmental infectious disease model structured by both race and age, incorporating empirically derived contact matrices to represent heterogeneity in social behavior. The model captures interactions across twelve demographic subgroups and enables the study of how behavioral mixing patterns shape disease transmission. While the inclusion of contact data explains a substantial portion of variation in group-level transmission dynamics, our results indicate that racial disparities persist beyond what can be attributed to behavioral contact patterns alone. This suggests the influence of unmeasured structural factors, such as differential susceptibility, healthcare access, or baseline risk. Our approach highlights the utility of structured modeling frameworks for uncovering the multi-layered mechanisms underlying population-level disparities in disease burden.

Organized by: Meredith Greer, Prashant Kumar Srivastava, Michael Robert (Bates College), Prashant Kumar Srivastava (Indian Institute of Technology, Patna) and Michael Robert (Virginia Tech)

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Lihong Zhao Kennesaw State University
   "Modeling the Dynamics of Legionnaries' Disease and Management Strategies"
Some pathogens can survive and replicate in abiotic environment outside the host systems and rely on the interaction with an environmental reservoir to transmit and infect hosts. Mathematical modeling can provide insights into the complex and often unknown dynamics of environmentally transmitted diseases. One such pathogen is the bacteria Legionella, the inhalation of this bacteria suspended in aerosolized water can lead to an atypical pneumonia which is known as the Legionnaries' disease (LD). In 2018, nearly 10,000 LD cases were reported in the United States. The true incidence should be higher as LD is underdiagnosed and underreported. In this talk, we will present the model we developed to examine the factors that may have contributed to the increase in LD outbreaks, and the insights into management strategies using control theory.
2. Tinashe Byron Gashirai (Postdoctoral Fellow) University of Idaho
   "A theory of risk perception in shaping human behavior to policy compliance during outbreaks"
The interplay of perceived risk of infection and protective behavior of the host in response to an emerging infection is complex and difficult to abstract. We therefore present a simple human behavior model based on the hypothesis that the human host engages in positive adaptive behavior when the disease prevalence reaches a certain threshold. Our mathematical analysis shows that the recruitment rate of susceptible individuals and the prevalence that triggers protective behavior influence the persistence or extinction of the disease. Moreover, abrupt changes in the transmission rate due to risk perception modulated host behavior may result in backward bifurcation. This complicates the control of the disease since the basic reproduction number fails to predict the occurrence of an epidemic. This study highlights the importance of understanding the role of complacency in engaging human adaptive response and risk perception in combating disease spread.
3. Claudia Pio Ferreira Unesp, IBB
   "Mathematical epidemiology and control of hospital-associated infections"
Healthcare-associated infections cause significant patient morbidity and mortality, and contribute to growing healthcare costs. Active surveillance systems, hospital staff compliance, including hand hygiene, and a rational use of antimicrobials are among the important measures to mitigate the spread of healthcare-associated infection within and between hospitals. Focusing on the role of patient movement within and between hospitals on the transmission and incidence of enterobacteria producing the K. pneumoniae Carbapenemase, we developed a metapopulation model where the connections among hospitals are made using a theoretical hospital network based on Brazilian hospital sizes and locations. The pathogen reproductive number, R_0 was calculated in different scenarios defined by both the links between hospital environments and between different hospitals. Furthermore, the efficacy of infection prevention and control on several hospital networks is assessed. Overall, the obtained results emphasize the importance of data collection on infection transmission and patient transfers, and show that the allocation of control units based on the R_0 of the hospitals may work better than the network-topology-based allocations.

Organized by: Folashade B. Agusto (University of Kansas), Chidozie Williams Chukwu

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Blessing Emerenini Rochester Institute of Technology, USA
   "Integrative Triple Therapy Against Bacterial Infections: Exploring Synergistic Dynamics"
Due to their adaptive resistance mechanisms against phages, immune responses, and antibiotics, bacterial biofilms pose considerable challenges to effective treatment, necessitating the development of innovative therapeutic strategies. In this work, we present a comprehensive triple combination therapy model that integrates bacteriophages, innate immune responses, and antibiotics within a highly nonlinear, deterministic, and spatiotemporal mathematical framework. We investigate a range of clinically relevant parameters, including antibiotic dosage and timing, phage administration strategies, and immune response intensity. The formulated model provides mechanistic insights into phage-bacteria dynamics, elucidates post-treatment biofilm structures, and informs precision treatment strategies, particularly for clinically accessible biofilm infections. By bridging clinical applications with advanced mathematical modeling, this work contributes to the development of more effective therapeutic interventions.
2. Olusegun Otunuga Augusta University, USA
   "Stochastic Modeling and First-Passage-Time Analysis of Oncological Time Metrics with Dynamic Tumor Barriers"
The first-passage-time (FPT) that a tumor size reaches a particular barrier is important in evaluating the efficacy of anti-cancer therapies and understanding certain oncological time occurrences. For certain verified stochastic models describing the volume of a tumor, a moving barrier for the tumor size in which an explicit solution of an FPT probability density function (PDF) exists for the first time the tumor size reaches the moving barrier is obtained in this work. The stochastic tumor dynamics incorporate anti-cancer therapies/treatments that are administered at varying rates. The first-passage-time density (FPTD) is derived and utilized to determine the time at which the tumor volume first reaches the moving barrier, providing a framework for analyzing various oncological time metrics. These metrics include key time measurements used to characterize tumor progression, evaluate treatment response, and capture recurrence patterns in cancer dynamics. The treatment effort needed to cause reduction in tumor size is also obtained. This work is applied to experimental data including the Murine Lewis Lung Carcinoma cells originally derived from a spontaneous tumor in twenty control mice. The time at which the volume of the tumor of each mouse doubles in size is estimated using the results obtained in this study.
3. Nourridine Siewe Rochester Institute of Technology, USA
   "A mathematical model of obesity-induced type 2 diabetes and efficacy of anti-diabetic weight reducing drug"
The dominant paradigm for modeling the obesity-induced T2DM (type 2 diabetes mellitus) today focuses on glucose and insulin regulatory systems, diabetes pathways, and diagnostic test evaluations. The problem with this approach is that it is not possible to explicitly account for the glucose transport mechanism from the blood to the liver, where the glucose is stored, and from the liver to the blood. This makes it inaccurate, if not incorrect, to properly model the concentration of glucose in the blood in comparison to actual glycated hemoglobin (A1C) test results. In this paper, we develop a mathematical model of glucose dynamics by a system of ODEs. The model includes the mechanism of glucose transport from the blood to the liver, and from the liver to the blood, and explains how obesity is likely to lead to T2DM. We use the model to evaluate the efficacy of an anti-T2DM drug that also reduces weight.
4. Joan Ponce University of Arizona, USA
   "Impact of DARC Polymorphism on P. vivax Transmission Dynamics"
The malarial parasite emph{Plasmodium vivax} has co-evolved with human populations for millennia. Genetic variants such as the FY(^*)O allele in the Duffy Antigen Receptor for Chemokines (DARC) and the sickle cell allele (HbS) have been naturally selected in malaria-endemic regions because they confer partial resistance to infection, enhancing the survival and reproductive success of carriers. As protective alleles rise in frequency, malaria incidence declines, reducing the selective pressure for further resistance. In this work, we develop a seasonally forced model that couples malaria transmission dynamics with the evolution of DARC genotype frequencies, using fast-slow analysis to capture the multiscale nature of these processes. We derive the basic reproduction number (R_0) and interpret it as a weighted sum of contributions from infected individuals of each genotype. Using data from the Amazonas region of Brazil---where DARC polymorphism remains prevalent and emph{P. vivax} cases persist---we calibrate the model and explore how changes in DARC genotype frequencies impact malaria burden. Our analysis determines the threshold proportion of Duffy-negative individuals required to achieve population-wide protection against emph{P. vivax}, and quantifies how varying levels of Duffy negativity affect monthly incidence patterns.

Organized by: Abba Gumel (University of Maryland), Alex Safsten, Alice Oveson (both University of Maryland)

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-2.

1. Jacques Bélair Université de Montréal
   "Knowledge as an Infection: Modeling Variable Compliance with Non-Pharmaceutical Interventions (NPIs)"
Management of the COVID-19 pandemic required, during its early stages, the deployment of non pharmaceutical interventions (NPIs) [social isolation, physical distancing, mask-wearing, hand-washing], and then, as they became available, administration of repeated doses of vaccine. We are interested in the consequences, for the dynamics of the disease, of variable adherence to these measures, and the motivation generating the lack thereof. We present two modeling approaches to represent this evolution of behaviour. First, a basic SEIRS model is expanded by introducing a structure in the infectious class, to reflect the variable severity of symptoms and the presence of asymptomatic cases considering the population divided into two classes according to their degree of adherence to the NPIs. Then, from a different perspective, we focus on the health literacy level in a population and the consequences, for the disease dynamics, of both knowledge dissemination and its integration in behaviour.
2. Asa Rishel University of Maryland
   "Mind Over Matter: Balancing the Benefits of COVID Lockdowns with Their Cost on Mental Health"
The COVID-19 pandemic took its toll not only on the physical health of those who lived through it, but also on their mental health. I will present a model of the direct and indirect effects of COVID-19 and the associated public policies on mental health. This is an SIRS model of COVID-19, with compartments for mild, acute, and chronic COVID-19 infections and additional compartments for populations with mental health symptoms. Parameters are determined based on fitting from the first wave of COVID-19 in the New York state population, which includes several changes in local government policy, e.g, lockdown orders, which have an effect on the rate at which mental health systems develop. Finally, an additional “delay” term is included in the model to account for the delay between lockdowns going into effect and individuals developing mental health symptoms. The goal of our analysis is to understand how government policy in response to a pandemic can seek to maximize the population's quality-adjusted life years (QALY), which is a measure not only of lifespan, but also the quality of the years lived. I will present some preliminary results suggesting the optimal timing and strength of government lockdown mandates.
3. Bryce Morsky Florida State University
   "Social Dynamics, Information Spread, and Behavioral Responses in Epidemic Modeling"
Social dynamics and the spread of information are critical factors in the spread of disease, influencing contact rates, behavior, and beliefs. This talk presents behavioral-epidemiological models featuring tipping-point dynamics for the uptake of vaccines or non-pharmaceutical interventions (NPIs), driven by real and perceived infection risks and social norms. These dynamics create collective action problems, leading to cycles of protective behavior and infections, with nonlinear responses to epidemiological parameters. The role of information dissemination is explored, particularly the roles of broadly shared information along with information bubbles.
4. Claus Kadelka Iowa State University
   "Adaptive Human Behavior and Delays in Information Availability Autonomously Modulate Epidemic Waves"
The recurrence of epidemic waves has been a hallmark of infectious disease outbreaks. Repeated surges in infections pose significant challenges to public health systems, yet the mechanisms that drive these waves remain insufficiently understood. Most prior models attribute epidemic waves to exogenous factors, such as transmission seasonality, viral mutations, or implementation of public health interventions. We show that epidemic waves can emerge autonomously from the feedback loop between infection dynamics and human behavior. Our results are based on a behavioral framework in which individuals continuously adjust their level of risk mitigation subject to their perceived risk of infection, which depends on information availability and disease severity. We show that delayed behavioral responses alone can lead to the emergence of multiple epidemic waves. The magnitude and frequency of these waves depend on the interplay between behavioral factors (delay, severity, and sensitivity of responses) and disease factors (transmission and recovery rates). Notably, if the response is either too prompt or excessively delayed, multiple waves cannot emerge. Our results further align with previous observations that adaptive human behavior can produce non-monotonic final epidemic sizes, shaped by the trade-offs between various biological and behavioral factors – namely, risk sensitivity, response stringency, and disease generation time. Interestingly, we found that the minimal final epidemic size occurs on regimes that exhibit a few damped oscillations. Altogether, our results emphasize the importance of integrating social and operational factors into infectious disease models, in order to capture the joint evolution of adaptive behavioral responses and epidemic dynamics.

Organized by: Amy Hurford (Memorial University), Michael Li, Public Health Agency of Canada

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-3, and Part-4.

1. Sally Otto University of British Columbia
   "Coupled dynamics and the challenge of estimating Rt in small jurisdictions"
During the COVID-19 pandemic, estimates of the reproductive number (Rt) or growth rate (r) from different jurisdictions were often surprisingly similar, given expected variation in contact rates. In this talk, I discuss how signatures of growth can be misleading in areas small jurisdictions and what we can learn from considering coupled dynamics with migration among areas.
2. Julien Arino University of Manitoba
   "Introduced cases and spread of infection in a community"
The recent COVID-19 pandemic made it clear that governments the world over would not hesitate to take public health measures of consequence to curtail the spread of pathogens. Among the myriad of measures used, travel interruptions, enhanced border control and quarantine, targeted specifically spatio-temporal spread. Sometimes, these travel measures were demonstrably useful, but altogether, the overall benefits remain debated. In order to quantify the effect of these measures, it is important to understand how disease introductions unfold in locations from which they are at that point absent. In particular, gaining some sense of the relative contributions of externally and locally generated cases is critical. To do this, we explore numerically a continuous-time Markov chain derived from a simple deterministic metapopulation model for case introduction.
3. Jude Kong University of Toronto
   "Human Behavior and Epidemic Dynamics: Adaptive vs. Robust Control Strategies in Shaping Outbreak Outcomes"
Human behavior significantly influences epidemic dynamics through complex interactions driven by risk perception and public health interventions. In this talk, we use a model of epidemic spread to examine how adaptive control strategies, where individuals dynamically adjust behaviors in response to trends like case doubling rates or awareness campaigns, influence disease transmission compared to robust control strategies that enforce fixed reductions in risky activities. We equally explore how behavioral adaptations, such as risk compensation—where perceived lower risks lead to increased risky behaviors—or risk homeostasis, where individuals maintain a constant level of acceptable risk, can undermine these control efforts. Our findings suggest that adaptive control strategies, by leveraging responsive behavioral changes, may offer a more effective approach to mitigating epidemic spread. These insights highlight the critical role of understanding and harnessing human behavioral dynamics in designing effective public health strategies for outbreak management.
4. Pouria Ramazi Brock University
   "Modeling Behavioral Heterogeneity to Optimize Vaccine Uptake Through Tailored Communication"
This talk explores how heterogeneity in individual decision-making influences vaccine uptake and how understanding this variation can enhance public health strategies. We distinguish between two primary behavioral types: evidence-based learners, who base their decisions on immediate personal payoff, and social-based learners, who are influenced by the observed experiences of others. The relative proportions of these two groups in a population fundamentally shape uptake dynamics. Through a mechanistic modeling framework and identifiability analysis, we demonstrate that these group proportions are not only theoretically identifiable but also practically estimable from vaccine uptake data. Our results show significant variation in these proportions across jurisdictions, suggesting that a one-size-fits-all communication strategy may be suboptimal. Tailoring messages to target specific behavioral profiles can more effectively promote vaccination and improve overall public health outcomes.

Organized by: Folashade B. Agusto (University of Kansas), Chidozie Williams Chukwu

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Chidozie Williams Chukwu Georgia Southern University, Statesboro, Georgia, USA
   "Dynamic Multi-country Modeling for Forecasting and Controlling Tuberculosis"
In this talk, we present a multi-country analysis of Tuberculosis (TB) epidemic model. We develop a deterministic TB model incorporating optimal control strategies and analyze its dynamics using mathematical tools. The model was calibrated using the new TB incidence data from India, Lesotho, Angola, and Indonesia. Numerical simulations are conducted to assess the impact of effective mask usage and case detection as intervention strategies. Our results project future trends of TB in the four countries studied. These insights are crucial for mitigating the spread of TB and addressing future challenges associated with potential TB outbreaks, particularly in the context of global public health crises.
2. Hewan Shemtaga, Selim Sukhtaiev, and Dr. Wenxian Shen Auburn University, USA
   "Logistic Keller-Segel chemotaxis models on compact graphs"
Chemotaxis phenomena governs the directed movement of micro-organisms in response to chemical stimuli. We investigate a pair of logistic type Keller–Segel systems of reaction-advection-diffusion equations modeling chemotaxis on networks. The distinction between the two systems is driven by the rate of diffusion of chemo-attractant. We prove the global existence of classical solution subject to Neumann-Kirchhoff vertex conditions without any conditions on chemotaxis sensitivity. In addition, we show that solutions with a non-negative and non-zero initial function converge to a globally stable constant solution for relatively small chemotaxis sensitivity. However, as chemotaxis sensitivity increase, we prove the constant solution loses stability and there exist other non-constant steady states bifurcating from the constant solution.
3. Ousmane Seydi University Le Havre, France
   "Growth Bounds and Threshold Dynamics in Periodic Structured Population Models"
Understanding when a population will grow, decline, or persist over time is a central question in mathematical biology. In this talk, we present a general method for identifying the conditions under which population growth occurs, even in models that incorporate age-structure, nonlocal interactions, or delays. Our approach applies to a broad class of mathematical systems, and we provide tools to compute critical threshold values—such as reproduction numbers—and to explain how these values determine the long-term behavior of the population. This framework draws on ideas from operator theory and dynamical systems to gain insight into biological processes that are periodic in time.
4. Daniel Cooney University of Illinois Urbana-Champaign, USA
   "Modeling Cross-Scale Evolutionary Dynamics"
Natural selection often operates simultaneously across multiple levels of biological organization, with evolutionary tensions often arising between traits or behaviors that are favored at different levels of selection. One common example of this tension arises in the evolution of altruism in group-structured populations, in which actions that are costly and result in an individual-level disadvantage while providing a collective benefit to the individual’s group. In this talk, we will explore a variety of PDE models that use evolutionary game theory to describe the evolution of altruism under competition occur both within and among groups, and we will discuss how different formulations of individual-level and group-level birth and death events can impact the long-time support for cooperation under these PDE models.

Organized by: Abba Gumel (University of Maryland), Alex Safsten, Arnaja Mitra (both University of Maryland)

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-2.

1. Casey O'Brien North Carolina State University
   "Modeling a Novel Gene Drive That Targets Immune Responses"
Gene drive technologies hold promise for controlling invasive pests, mitigating disease transmission, and protecting local ecosystems and agriculture. However, their deployment hinges on resolving safety concerns, particularly the risk of unintended spread into non-target populations. Current confinement strategies rely largely on invasion thresholds which take advantage of unstable equilibrium points in allele frequency, below which the drive will not spread. This maintains local confinement by preventing migrants from spreading the drive in surrounding populations. While this is an effective strategy for gene drives meant to introduce a trait to a population, its success has been more limited in suppression gene drives. We circumvent this issue by designing a novel suppression drive system that targets the immune response of an organism to a local stressor (i.e., endemic virus, fungus, or a specialized parasitoid). The drive system increases the target organism’s susceptibility to the stressor by increasing the likelihood of acquiring the infection or the impact of infection on the organism. This means that the drive system’s fitness cost is dependent on the abundance of the stressor. We model several drive systems to consider the efficacy of the system in different settings
2. Jackson Champer Peking University
   "Suppression gene drive for mosquito control: large scale spatial models and impact on disease transmission"
Gene drive alleles bias inheritance in the favor, allowing them to quickly spread throughout a population. They could combat disease by rapidly spreading a cargo gene that blocks pathogen transmission, or they could directly suppress vector populations. Progress has been made to reduce resistance allele formation, a main obstacle to successful gene drive in Anopheles stephensi mosquitoes, yielding efficient systems. However, computational analysis using individual-based models predicts that suppression drives may still not succeed in spatially structured natural populations due to the 'chasing' phenomenon that causes chaotic, long-term persistence of both drive and wild-type alleles. To assess this effect on malaria transmission, we developed a deep-learning model to allow assessment of many drive, ecology, and disease parameters without a large computational burden. We found that malaria could potentially be eliminated even if the mosquito population persists. Thus, despite unexpected complexity, gene drive remains a potentially powerful method to reduce malaria infections.
3. Daihai He The Hong Kong Polytechnic University
   "Resolving the enigma of Iquitos and Manaus: A modeling analysis of multiple COVID-19 epidemic waves in two Amazonian cities"
The nearby cities of Iquitos (Peru) and Manaus (Brazil) experienced the world’s highest infection and mortality rates during the first COVID-19 wave in 2020. Key studies suggested that >70% of the city populations were infected in this wave and thus close to herd immunity and protected. It remains an enigma as to why a deadly second wave followed in Manaus worse than the first. To resolve this, we present a data-driven model of epidemic dynamics in Iquitos which we use to help explain and model events in Manaus. The partially observed Markov process model simultaneous fits a flexible “variable R0”, estimates long-term immunity waning and impulsive immune evasion, and thus provides a comprehensive framework for characterizing and modeling new variants of concern.

Organized by: Amy Hurford (Memorial University), Michael Li, Public Health Agency of Canada

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-2, and Part-4.

1. Wade McDonald University of Saskatchewan
   "Use of Synthetic Data to Improve Wastewater-based Epidemiological Models in a Small Jurisdiction"
Previous studies have shown that applying methods such as Particle Filtering and Particle Markov-Chain Monte Carlo (pMCMC) to stochastic mechanistic epidemiological models can enhance model accuracy compared to simple parameter calibration. Addition of data streams to the filter can improve model fit even if those data are deemed to be of “low quality,” e.g., internet search volumes. In the present work, we employ a synthetic dataset, generated by an agent-based model, to explore the use of pMCMC with a compartmental epidemiological model, including wastewater-based epidemiology (WBE), in the context of a small jurisdiction facing an emerging pathogen. Predictive performance of the filtered model will be compared against synthetic ground truth using clinical cases alone versus clinical cases and WBE measures. Effects of structural mismatches between the synthetic ground truth and filtered model will be considered; for example, what if the synthetic ground truth admits waning of immunity (SIRS) but our filtered model assumes immunity is permanent (SIR)?
2. Matthew Betti Mount Allison University
   "Modeling healthcare demand during a disease outbreak"
One of the driving concerns during any epidemic is the strain on the healthcare system. During severe outbreaks, healthcare systems can become quickly overwhelmed. We develop a healthcare demand module that can take epidemiological data and healthcare parameters and can forecast number of doctor visits, hospital occupancy. Using real-world data we can estimate the length of stay of hospitalized individuals. The module can be extended to account for pharmaceutical and PPE usage at differing levels of conservation.
3. Sicheng Zhao McMaster University
   "Edge-based Modeling for Disease Transmission on Random Graphs – an Application to Mitigate a Syphilis Outbreak"
Edge-based random network models, especially those based on bond percolation methods, can be used to model disease transmission on complex networks and accommodate social heterogeneity while keeping tractability. Here we present an application of an edge-based network model to the spread of syphilis in the Kingston, Frontenac and Lennox & Addington (KFL&A) region of Southeastern Ontario, Canada. We compared the results of using a network-based susceptible-infectious-recovered (SIR) model to those generated from using a traditional mass action SIR model. We found that the network model yields very different predictions, including a much lower estimate of the final epidemic size. We also used the network model to estimate the potential impact of introducing a rapid syphilis point of care test (POCT) and treatment intervention strategy that has recently been implemented by the public health unit to mitigate syphilis transmission.
4. Caroline Mburu British Columbia Centre for Disease Control/Simon Fraser University
   "Wastewater-based modelling for Mpox surveillance among gbMSM in BC"
Background: The 2022 global outbreak of Mpox, caused by Clade IIb of the monkeypox virus (MPXV), primarily affected gay, bisexual, and other men who have sex with men (gbMSM). While clinical case surveillance has been central to the public health response, it faces limitations due to underreporting, social stigma, and asymptomatic infections. To complement case-based surveillance, wastewater-based surveillance (WBS), which had been valuable in monitoring other infections, including during the COVID-19 pandemic, was adopted to track MPXV circulation. Several studies have demonstrated correlations between MPXV viral loads in wastewater and reported Mpox cases, supporting the utility of WBS for population-level monitoring. In parallel, mechanistic models based solely on clinical case data have provided insights into Mpox transmission dynamics and the impact of interventions such as vaccination and behavioral change. However, to date, no modeling framework has integrated both data streams to jointly infer Mpox transmission dynamics. As a result, the mechanistic relationship between viral load in wastewater and underlying disease transmission remains poorly understood, particularly in the context of evolving behavioral patterns and vaccination uptake Methods: We developed a compartmental model to simulate Mpox transmission within the gbMSM population, incorporating heterogeneity through stratification by levels of sexual activity. The model integrates key data streams, including clinical case notifications, MPXV viral load signals from WBS, sexual network data and vaccination coverage. The framework explicitly incorporates viral shedding dynamics into wastewater, allowing for the exploration of the relationship between underlying infections and observed WBS signals. We use this model to evaluate the conditions under which wastewater viral load may act as leading or lagging indicators of reported cases, considering factors such as reporting delays, underreporting, asymptomatic infections, changes in sexual behavior, and the rollout of vaccination programs. Conclusions: This study bridges clinical and environmental surveillance through a mechanistic framework tailored to behaviorally structured populations. By jointly modeling case and WBS data, we aim to improve the interpretation of wastewater signals and support more accurate assessments of transmission in hard-to-reach or underreported populations. Findings will inform public health decision-making around Mpox surveillance and preparedness, particularly in contexts where traditional case-based reporting is limited.

1. Lindsay Keegan University of Utah
   "A theoretical framework to quantify the tradeoff between individual and population benefits of expanded antibiotic use"
The use of antibiotics during a disease outbreak presents a critical tradeoff between immediate treatment benefits to the individual and the long-term risk to the population. Typically, the extensive use of antibiotics has been thought to increase selective pressures, leading to resistance. This study explores scenarios where expanded antibiotic treatment can be advantageous for both individual and population health. We develop a mathematical framework to assess the impacts on outbreak dynamics of choosing to treat moderate infections not treated under current guidelines, focusing on cholera as a case study. We derive conditions under which treating moderate infections can sufficiently decrease transmission and reduce the total number of antibiotic doses administered. We identify two critical thresholds: the Outbreak Prevention Threshold (OPT), where expanded treatment reduces the reproductive number below one and halts transmission, and the Dose Utilization Threshold (DUT), where expanded treatment results in fewer total antibiotic doses used than under current guidelines. For cholera, we find that treating moderate infections can feasibly stop an outbreak when the untreated reproductive number is less than 1.42 and will result in fewer does used compared to current guidelines when the untreated reproductive number is less than 1.53. These findings demonstrate that conditions exist under which expanding treatment to include moderate infections can reduce disease spread and the selective pressure for antibiotic resistance. These findings extend to other pathogens and outbreak scenarios, suggesting potential targets for optimized treatment strategies that balance public health benefits and antibiotic stewardship.
2. Francisca Olajide University of Ottawa
   "From process to structure of EWSs"
The emergence of infectious diseases remains a huge challenge to public health. Early detection of outbreaks using early warning signals (EWSs) offers an invaluable opportunity for effective preparedness and disease management. In this study, we seek to understand the structure of these signals using a mechanistic model that captures epidemic and social processes. We analyzed the simulated time series for change points and EWSs (autocorrelation and variance). All time series showed the expected delay in that the detected change point occurred significantly after the parameter passed the bifurcation point. These early warning signals exhibited a stronger response after the threshold for disease emergence had been exceeded. Assessing different disease progression and intervention models will help determine the most effective signals for use in public-health settings.
3. Marwa Tuffaha York University
   "Counterfactual COVID-19: Modeling Alternative Mitigation and Vaccination Policies for Canada"
COVID-19, a global pandemic with severe health and economic repercussions, has prompted various approaches to mitigate its impact. We adapt an age-structured SEIVS model—incorporating waning immunity and partial protection—to explore counterfactual scenarios of non-pharmaceutical interventions (e.g., school/workplace closures, distancing) and selected vaccine policy changes in Canada. By altering contact patterns and compliance levels, we assess potential outcomes under stricter, earlier, or more relaxed mitigation measures, with a lesser emphasis on shifting vaccination rollouts. Findings indicate that timely, robust mitigation can substantially reduce severe disease and delay epidemic peaks, whereas delayed or minimal interventions lead to higher case burden. Integrating vaccine strategies into these scenarios further highlights the interplay between pharmaceutical and non-pharmaceutical measures, showcasing how modeling can inform dynamic policy-making for ongoing and future public health crises.

1. Zitao He University of Waterloo
   "Leveraging deep learning and social heterogeneity to detect early warning signals of disease outbreaks"
Identifying early warning signals (EWS) of shifts in vaccinating behaviors can be helpful in predicting disease outbreaks. Evolutionary game theory has been used to model individual vaccination decisions, while bifurcation theory has identified statistical EWS, such as increasing variance and lag-1 autocorrelation, near critical transitions. However, these conventional methods often struggle with noisy data. In this study, we improve coupled behavior-disease models by incorporating population heterogeneity, distinguishing between social media users and non-users, and examining the role of homophily in shaping disease dynamics. We develop deep learning classifiers, including Long Short-Term Memory (LSTM) and Residual Neural Networks (ResNet), trained on simulated data from a stochastic coupled model with Lévy noise that captures the heavy-tailed fluctuations characteristic of real-world systems. Our results show that these models outperform traditional statistical indicators in both sensitivity and specificity while offering clearer interpretability on empirical data. This approach provides a robust framework for detecting EWS and improving outbreak prediction, highlighting the power of deep learning in real-time public health monitoring.
2. Soyoung Kim National Institute for Mathematical Sciences (NIMS)
   "Optimizing Vaccine Efficacy Trials for Emerging Respiratory Epidemics: A Mathematical Modeling Approach"
Evaluating vaccine efficacy (VE) during emerging epidemics is challenging due to unpredictable transmission dynamics. An age-structured SEIAR compartmental model was developed using South Korea’s 2022 population and parameters from COVID-19 and the 2009 H1N1 pandemic to optimize RCT timing and sample size. Simulations varied trial initiation (±10%, ±20%, ±30% of the epidemic peak), follow-up (4–12 weeks), recruitment (2–12 weeks), and non-pharmaceutical interventions (10–20%). Results showed that VE remained stable, but sample size requirements fluctuated, decreasing post-peak before rising sharply. Starting trials 30% before the peak with extended recruitment minimized sample sizes without compromising power. NPIs expanded trial feasibility, and sample size estimates from simulated placebo cases maintained >85% power, avoiding under- or over-powering. This model provides a framework for designing adaptive and efficient vaccine trials in future respiratory epidemics.
3. Jonggul Lee National Institute for Mathematical Sciences
   "Quantifying Shifts in Social Contact Patterns: A Post-Covid Analysis in South Korea"
Social contact patterns are crucial for understanding infectious disease transmission, but detailed data has been scarce in South Korea. We conducted a two-week survey covering various periods, including school vacations and holidays. Participants provided information on their contacts, including location, duration, frequency, and characteristics of the contact person. Analysis of the data from 1,987 participants revealed 133,776 contacts, averaging 4.81 contacts per person daily. Contact numbers varied by age, household size, and time period. The highest number of contacts was observed in the 5-19 age group, lowest in the 20-29 group, and gradually increased up to the 70+ group. Larger households tended to have more contacts. Contact patterns differed significantly across time periods. Weekdays during the school semester showed the highest number of contacts, followed by weekdays during vacations, the Lunar New Year holidays, and weekends. During the Lunar New Year, there was an increase in contacts with extended family members, enhancing subnational social mixing. These findings provide valuable insights into social contact patterns in South Korea, which can improve our understanding of disease transmission and aid in developing region-specific epidemiological models.
4. Andrew Omame York University Toronto, Canada
   "Pre-exposure vaccination in the high-risk population is crucial in controlling mpox resurgence in Canada"
As mpox spread continues across several endemic and non-endemic countries around the world, vaccination has become an integral part of the global response to control the epidemic. Some vaccines have been recommended for use against mpox by the World Health organization (WHO). As the roll-out of mpox vaccines continue across the globe, it is imperative to develop mathematical models to support public health officials and governments agencies in optimizing vaccination strategies to curtail the resurgence of mpox. In this article, we develop a compartmental mathematical model to investigate the impact of vaccination in controlling a potential mpox resurgence in Canada. The model categorizes individuals into high- and low-risk groups and incorporates pre-exposure vaccination in the high-risk group and post-exposure vaccination in the high- and low-risk groups. The vaccine-free version of the model was calibrated to the daily reported cases of mpox in Canada from April to October 2022, from which we estimated key model parameters, including the sexual and non-sexual transmission rates. Furthermore, we calibrated the full model to the daily reported cases of mpox in Canada in 2024, to estimate the current mpox vaccination rates in Canada. Our results highlight the importance of pre-exposure vaccination in the high-risk group on controlling a potential resurgence of mpox in Canada, and the minimal effects of post-exposure vaccination in the high- and low-risk groups on the outbreak. In addition, our model predicts the possibility of mpox becoming endemic in Canada, in the absence of pre-exposure vaccination in the high-risk group. Overall, our modeling result suggests that pre-exposure vaccination in the high-risk group is crucial in controlling mpox outbreak in Canada. Stepping up this vaccination is sufficient to avert a potential mpox resurgence in Canada.

1. Alexander Meyer University of Notre Dame
   "Estimating pathogen introduction rates from serological data to characterize past and future patterns of transmission"
The unpredictable timing of infectious disease outbreaks poses significant challenges for public health preparedness. For many pathogens, this unpredictability is due to uncertainty regarding introduction rates—the frequency with which the pathogen is introduced into at-risk populations. We present three model-driven advances toward quantifying pathogen introduction rates and their effects on outbreak timing and size. Our method relies on the assumption that pathogen introductions can only cause large outbreaks when population immunity is sufficiently low (i.e., the reproduction number R(t) > 1). First, we demonstrate that, for pathogens that cause lifelong immunity, introduction rates can be estimated from age-structured serological data. Second, we estimate annual rates of chikungunya virus (CHIKV, a mosquito-borne pathogen) introductions into 17 populations in Africa and Asia using serological data collected between 1973 and 2015. Our median estimates ranged from 1 to 70 CHIKV introductions per 10 million people per year. Finally, we used simulations to show how the introduction rate of a pathogen can shape its transmission patterns over time in affected populations. A lower introduction rate allows population immunity to wane between introductions, leading to large but infrequent outbreaks. In contrast, a higher introduction rate causes frequent low-level transmission, resulting in elevated population immunity that precludes large outbreaks. Together, these results illustrate how age-structured serology, a common type of epidemiological data, can be leveraged to better understand both historical and future transmission patterns in different populations.
2. Binod Pant Northeastern University
   "Could malaria mosquitoes be controlled by periodic release of transgenic mosquitocidal Metarhizium pingshaense? A mathematical modeling approach"
Mosquito-borne diseases, such as malaria, remain a major global health challenge, necessitating the exploration of innovative vector control strategies. Naturally occurring entomopathogenic fungi have been shown to reduce mosquito lifespan, but their slow-acting nature has limited their practical application. Advances in biotechnology have led to the development of transgenic fungus strains (this study will focus on Metarhizium pingshaense strain) engineered to express insecticidal toxins, significantly increasing their efficacy against malaria vector mosquitoes. To our knowledge, this is the first deterministic model designed to assess the impact of fungal-based mosquito control. The proposed model accounts for multiple transmission pathways of the fungal infection, including mating-based transmission from infected males to females and indirect transmission via contact with infectious mosquito carcasses. The model is analyzed to determine equilibrium states, local stability conditions, and the reproduction number. Numerical simulations explore various release scenarios, evaluating the effectiveness of periodic versus continuous fungal release in different ecological settings. The results indicate that transgenic Metarhizium pingshaense has the potential to significantly reduce mosquito populations, particularly when release strategies are optimized.
3. Soyoung Park University of Maryland
   "Mathematical assessment of the roles of vaccination and Pap screening on the incidence of HPV and related cancers in South Korea"
Human Papillomavirus (HPV) is a major sexually-transmitted infection that causes various cancers and genital warts in humans. In addition to accounting for about 99% of cervical cancer cases, it significantly contributes to anal, penile, vaginal, and head and neck cancers. Although HPV is vaccine-preventable (and highly efficacious vaccines exist for preventing infection with some of the most oncogenic HPV subtypes in the targeted population), the disease continues to cause major public health burden globally (largely due to inequity in access to the main control resources (i.e., access to Pap smear and vaccination) and low vaccination coverage in most communities that implement routine HPV vaccination). This lecture is based on the use of a new mathematical model (for the natural history of HPV, together with the associated neoplasia) for assessing the combined population-level impacts of Pap cytology screening and vaccination against the spread of HPV in a heterogeneous (heterosexual and homosexual) population. The model, which takes the form of a deterministic system of nonlinear differential equations, will be calibrated and validated using HPV-related cancer data from South Korea. Theoretical and numerical simulation results will be presented. Conditions for achieving vaccine-derived herd-immunity threshold (for achieving HPV elimination in Korea) will be derived.
4. Rosemary Omoregie University of Benin, Nigeria
   "Mathematical Model For Dengue and its Co-Endemicity with Chikungunya virus"
A deterministic nonlinear mathematical model describing the population dynamics for Dengue and Chikungunya virus taken into consideration the effect of misdiagnosis due to the co-endemicity of the two viruses in the human population. It is necessary to understand the most important parameters involved in their dynamics that may help in developing strategies for prevention, control and joint treatments. The model is rigorously analyzed qualitatively and thresholds for eradication are established.

1. Somdatta Sinha Indian Institute of Science Education Research
   "Compositional Complexity in Genomic Patterns and Classification"
A genome consists of a long string of four letters (bases A, T, C, G). How the information of biochemical processes stored in this string of bases is an open question. Are their higher order structures, such as, words, sentences, semantics, and a grammar in the DNA language (compositional complexity)? DNA from different species exhibit differences in global sequence composition, and this is used as markers to align larger sequences - grouping of genomes based on homology. Classification of genomes through similarity and dissimilarity is at the heart of Phylogenetics/Genomic Epidemiology. It uses several statistical-mathematical methods to align and compare the base sequences of multiple genomes, which are both computational resource intensive and time consuming for similar sequences. We develop and use an “alignment-free” method based on the Chaos-Game-Representation (CGR) of Statistical Physics, to successfully classify very closely related genomes of sub and sub-sub-species of HIV1 and mutants of Covid19. This useful approach requires less computational resources and time for analysis.
2. Qi Deng York University
   "Exploring the potential impact of a chlamydia vaccine in the US population using an agent-based model"
Chlamydia trachomatis (CT) infection is the most reported bacterial sexually transmitted infection (STI) in the United States (US). Despite many cases being asymptomatic, infection can lead to complications such as pelvic inflammatory disease (PID) in females, and infertility in both females and males. We developed an agent-based transmission model to evaluate the impact of a potential CT vaccine on the prevalence of CT infections and associated PID in the US population. The model simulates an evolving sexual network of 10,000 sexually active agents aged 15–54, including heterosexuals, female sex workers, and men who have sex with men, following Susceptible–Exposed–Infected–Recovered–Susceptible (SEIRS) transmission dynamics. A key strength of the model is its rigorous two-step calibration procedure, which first matches real CT prevalence by age and sex, followed by real PID prevalence by age in the US. This ensures realistic alignment with epidemiological patterns. The model incorporates both vaccination and test-and-treat strategies, enabling direct comparisons between interventions. We then evaluated the impact of different scenarios of vaccination coverage and targeting, assuming a vaccine with 80% efficacy against infection and a 5-year duration of protection. The results demonstrate a gender-neutral vaccine recommendation is projected to achieve the highest impact in reducing CT prevalence and PID burden, even with a moderate vaccination coverage. Beyond CT, this is flexible, computationally efficient framework is adaptable to study other STIs and assess the effectiveness of various intervention strategies, given appropriate epidemiological and behavioral data. By providing actionable insights, this framework serves as a decision-support tool for policymakers, public health officials, and vaccine developers.
3. Woldegebriel Assefa Woldegerima York University
   "Singular Perturbation Analysis of a Two-Time Scale Model of Vector-Borne Disease"
Biological systems evolve across different spatial and temporal scales. Modeling such complex systems gives rise to multi-scale differential equations that may be written as ODEs, PDEs, DDEs, SDEs, or Difference Equations. Particularly, vector-borne disease models are often described using ordinary differential equations with multiple time scales, which can involve singular perturbations—situations where rapid transitions or significant changes in system behavior occur due to small parameter variations or the interaction between fast and slow dynamics. To analyze these multi- time scale problems, we employ tools such as Geometric Singular Perturbation Theory (GSPT), Tikhonov’s Theorem, and Fenichel’s Theory. These methods provide insights into complex phenomena, including the loss of normal hyperbolicity and other intricate behaviors. Particularly, applying singular perturbation theory to vector-borne diseases allows us to reduce the dynamics to a one-time scale and understand their dynamics. To illustrate this, we present a Zika virus model and apply Tikhonov’s theorem and GSPT to investigate the model’s asymptotic behavior. Additionally, we conduct a bifurcation analysis to explore how the system’s behavior changes with variations in the parameter . We illustrate the various qualitative scenarios of the reduced system under singular perturbation. We will show that the fast–slow models, even though in nonstandard form, can be studied by means of GSPT.
4. Sarita Bugalia The University of Arizona
   "Modeling the Impact of Social Behavior, Under-Reporting, and Resources on Tuberculosis During COVID-19"
Despite being curable and preventable, tuberculosis (TB) still causes the highest mortality rates in the human population. However, the number of TB cases significantly reduced globally in 2020, according to the Global Tuberculosis Report by the World Health Organization, coinciding with the COVID-19 pandemic. These reductions in TB cases are likely due to a complex interplay between disruptions in TB health services and the case counts resulting from COVID-19. We developed a compartmental model for the co-infection of tuberculosis and COVID-19 in the human population to assess the impact of medical resources, mobility, under-reporting, and the social behavior (follow social distancing and face mask) of infected individuals with either disease. We computed the basic reproduction numbers for TB alone, COVID-19 alone, and the co-infection scenario. Additionally, key parameters and basic reproduction numbers were estimated by utilizing case studies from low-income, middle-income, and high-income countries in a multi-patch scenario. Our results indicate that increased social behavior among infected individuals significantly reduces the number of co-infected individuals. The impact of mobility was assessed using a two-patch model with emigration and immigration rates. It shows that the mobility of unreported infectious individuals significantly increases both active cases of TB and COVID-19. This study provides significant recommendations for medical providers and public health officials regarding TB elimination in high-income countries and TB reduction in lower-income countries with a high disease burden. The findings are also relevant for studying TB in the context of future pandemic scenarios.

1. Jongmin Lee Department of Mathematics, Konkuk University
   "How to Deal with the Health-economy Dilemma during a Pandemic: Research Framework and User-interactive Dashboard"
During the early stages of the COVID-19 pandemic, it was important to minimize both medical and economic costs. In this study, we introduce a machine learning-based multi-objective optimization framework that can propose cost-effective social distancing strategies. Our approach finds Pareto solutions that balance different goals, like reducing infections and minimizing social distancing costs. Then, the cost-benefit analysis can adjust each cost factor—for example, value of statistical life (VSL), fatality rate, or GDP. We also provide an interactive web dashboard so that policymakers and the public can test various scenarios easily. We tested this framework on the COVID-19 pandemic in Korea. The results show that the difference between the cost-optimal strategy and implemented strategy is 10% in cost. Notably, our results reveal two distinct patterns in cost-optimal solutions. When social distancing cost is proportional to intervention intensity, an on-off lockdown strategy proves most economical. In contrast, when the cost increases sharply with intensifying social distancing, maintaining a consistently moderate level of intervention minimizes overall expenses. By letting people explore different cost settings and intervention strategies, this tool can support more balanced decisions during emerging infectious disease crises in the future.
2. Arsene Brice zotsa ngoufack Université du Québec à Montréal
   "Stochastic epidemic model with memory on the previous infection and with varying infectivity and waning immunity"
After an individual has been infected by a pathogen, T lymphocytes store information about the pathogen. Consequently, upon reinfection by the same pathogen, an immune response memory is triggered. This immune memory allows the body to react very quickly against the pathogen. Indeed, when an individual recovers from a virus, sometimes the individual acquires full immunity. In some cases, the individual's immunity persists for some period, after which it decreases progressively and can even disappear. I will then present a stochastic epidemic model with memory on the previous infection, incorporating varying infectivity and waning immunity. More precisely, we will present a functional law of large numbers when the size of the population tend to infinity. We will also present results on the behaviour of the epidemic, more precisely the threshold for the existence of an endemic equilibrium, and study the stability of the endemic equilibrium.
3. Woldegebriel Assefa Woldegerima York University
   "The Mathematics of Deep Neural Networks with Application in Predicting the Spread of Avian Influenza Through Disease-Informed Neural Networks (DINNs)"
Deep learning has emerged in many fields in recent times where neural networks are used to learn and understand data. This study combines deep learning frameworks with epidemiological models and is aimed specifically at the creation and testing of DINNs with a view to modeling the infection dynamics of epidemics. Our research thus trains the DINN on synthetic data derived from an SI-SIR model designed for Avian influenza and shows the model’s accuracy in predicting extinction and persistence conditions. In the method, a twelve hidden layer model was constructed with sixty-four neurons per layer and ReLU activation function was used. The network is trained to predict the time evolution of five state variables for birds and humans over 50,000 epochs. The overall loss minimized to 0.000006, characterized by a combination of data and physics losses, enabling the DINN to follow the differential equations describing the disease progression.
4. Asa Rishel University of Maryland, College Park
   "Mind over matter: balancing the benefits of COVID lockdowns with their cost on mental health"
The COVID-19 pandemic took its toll not only on the physical health of those who lived through it, but also on their mental health. I will present a model of the direct and indirect effects of COVID-19 and the associated public policies on mental health. This is an SIRS model of COVID-19, with compartments for mild, acute, and chronic COVID-19 infections and additional compartments for populations with mental health symptoms. Parameters are determined based on fitting from the first wave of COVID-19 in the New York state population, which includes several changes in local government policy, e.g, lockdown orders, which have an effect on the rate at which mental health systems develop. Finally, an additional “delay” term is included in the model to account for the delay between lockdowns going into effect and individuals developing mental health symptoms. The goal of our analysis is to understand how government policy in response to a pandemic can seek to maximize the population's quality-adjusted life years (QALY), which is a measure not only of lifespan, but also the quality of the years lived. I will present some preliminary results suggesting the optimal timing and strength of government lockdown mandates.