Organized by: Mitchel J. Colebank (University of South Carolina), Vijay Rajagopal, The University of Melbourne, Australia

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

1. Mette Olufsen North Carolina State University
   "An uncertainty aware framework for generating vascular networks from imaging"
A well-calibrated mathematical model and an understanding of uncertainties in model predictions are essential for generating a digital twin. Creating a patient-specific cardiovascular model typically involves two key steps: (i) constructing the vascular domain and (ii) performing hemodynamic simulations. The vascular domain is usually obtained by segmenting CT or MRI scans to reconstruct the vascular network. Once constructed, hemodynamic simulations are conducted using inferred model parameters that minimize discrepancies between computed results and available physiological data. This talk will addres challenges in generating 1D network models with multiple branching generations and detecting abnormalities within these networks. One significant challenge is the automatic extraction of vessel centerlines, which is crucial for 1D modeling. We focus on a skeletonization-based method for centerline extraction, which iteratively removes voxels until only a single-voxel-wide path remains within each vessel. Using statistical change-point analysis, we construct a labeled directed graph (a tree) that encodes vessel connectivity, radii, and lengths. By sampling from normal distributions of these quantities with a 1D fluid dynamics model, we explore how uncertainties in geometry affect hemodynamic predictions. Our results emphasize the importance of accounting for image-based uncertainty in medical modeling.
2. Sara Johnson University of Puget Sound
   "Modeling Microglial Response to MCAO-Induced Ischemic Stroke"
Neuroinflammation immediately follows the onset of ischemic stroke in the middle cerebral artery. During this process, microglial cells are activated in and recruited to the penumbra. Microglial cells can be activated into two different phenotypes: M1, which can worsen brain injury; or M2, which can aid in long-term recovery. In this study, we contribute a summary of experimental data on microglial cell counts in the penumbra following ischemic stroke induced by middle cerebral artery occlusion (MCAO) in mice and compile available data sets into a single set suitable for time series analysis. Further, we formulate a mathematical model of microglial cells in the penumbra during ischemic stroke due to MCAO. Through use of global sensitivity analysis and Markov Chain Monte Carlo (MCMC)-based parameter estimation, we analyze the effects of the model parameters on the number of M1 and M2 cells in the penumbra and fit identifiable parameters to the compiled experimental data set. We utilize results from MCMC parameter estimation to ascertain uncertainty bounds and forward predictions for the number of M1 and M2 microglial cells over time. Results demonstrate the significance of parameters related to M1 and M2 activation on the number of M1 and M2 microglial cells. Simulations further suggest that potential outliers in the observed data may be omitted and forecast predictions suggest a lingering inflammatory response.
3. Simon Walker-Samuel University College London
   "Using physics-informed deep generative learning to model blood flow in the retina"
Disruption of retinal vasculature is linked to various diseases, including diabetic retinopathy and macular degeneration, leading to vision loss. We present here a novel algorithmic approach that generates highly realistic digital models of human retinal blood vessels, based on established biophysical principles, including fully-connected arterial and venous trees with a single inlet and outlet. This approach, using physics-informed generative adversarial networks (PI-GAN), enables the segmentation and reconstruction of blood vessel networks with no human input and which out-performs human labelling. Segmentation of DRIVE and STARE retina photograph datasets provided near state-of-the-art vessel segmentation, with training on only a small (n = 100) simulated dataset. Our findings highlight the potential of PI-GAN for accurate retinal vasculature characterization, with implications for improving early disease detection, monitoring disease progression, and improving patient care.
4. Mitchel Colebank University of South Carolina
   "Effects of vasomotor tone on systemic vascular wave reflections"
One-dimensional, pulse-wave propagation models are able to replicate hemodynamic waveforms that are representative of measured data. While these models are a potential tool in the era of digital twins, few models have considered the role of smooth muscle vasoactivity and its effects on blood pressure and flow. This is especially important for understanding cerebrovascular function, especially in diseases like dementia and Alzheimer's, where cerebral vasoactivity is known to be a cause and consequence of altered mechanical stimuli. Thus, there is a need for new computational models that explicitly account for vascular tone during hemodynamic simulation. Here, we implement a relatively simplistic exponential model of the proximal vasculature pressure-area relationship which incorporates extracellular matrix stiffness, vascular smooth muscle cell stiffness, the degree of vasomotor tone in comparison to some reference tone, and the reference pressure. We couple this vasoactive large vessel model to the structured tree boundary condition, which represents the microvascular beds. To differentiate between proximal and small vessel vasoconstriction, we also introduce a vasodilation factor in the structured tree that controls microvascular radii. We analyze the model using global sensitivity analysis, and provide insight into the distinct contributions of large and small vessel vasoactivity in an idealized systemic arterial network. Our results show that microvascular vasoconstriction is more impactful that proximal vessel vasotone, but that stress-strain behavior in the large vessels can be modulated divergently depending on the relative magnitudes of ECM and smooth muscle stiffness. This study lays the foundation for future studies investigating the effects of vasoactivity on hemodynamic outcomes.

Organized by: Joshua S. Weitz (University of Maryland, Department of Biology & Physics and U of Maryland Institute for Health Computing), Asher Leeks, University of British Columbia, Department of Zoology

1. Antoni Luque University of Miami
   "Impact and prediction of phage decay in natural microbial communities"
Phage decay is a key factor in the ecology and evolution of phages and their bacterial hosts. However, estimating the phage decay of different viruses in a community remains challenging. In this talk, I will share the approach that my lab is developing to address this problem. It relies on three complementary strategies. First, I will introduce a new transient dynamic method that facilitates identifying when phage decay and other processes are relevant in the community and under what circumstances a tipping point is expected to occur and significantly impact the community’s dynamics. Second, I will share the multiscale methods we are integrating to obtain phage decay rates for different phages from genomic data. This step relies strongly on the ability to identify structural proteins in metagenomes and the combination of several biophysical models. Third, I will show our initial attempts to relate our modeling approaches to phage decay experiments from aquatic environmental communities. I will conclude by emphasizing how the strategies discussed here could be valuable for other viruses and for optimizing phage biotechnological applications.
2. Asher Leeks University of British Columbia
   "Modelling the dynamics of cheating in natural populations of filamentous phages"
Diverse species of filamentous phages are found across natural environments, often encoding bacterial virulence traits, antimicrobial resistance, and novel metabolic capacity. In the laboratory, filamentous phages are vulnerable to cheating: mutants spontaneously emerge which have deleted shared gene products, and as a result can out-replicate full-length cooperative phages in coinfection. If these cheat mutants also emerge and spread in natural filamentous phage populations, this would have profound consequences for our understanding of phage population dynamics, and the dependent ecological and pathogenic consequences. However, it is difficult to detect cheating in natural populations for two key reasons: we lack longitudinal data, and so cannot directly measure the fitness of putative cheats; and most filamentous phage species are known only from sequence data, hence we cannot predict a priori which genes might have been deleted by cheats. Here, we use a quantitative approach to overcome these limitations, in order to measure cheating in natural filamentous phage populations. We construct a birth-death model that incorporates mutation, demographic noise, and a frequency-dependent selective advantage to cheating. We explicitly model the distribution of genome lengths expected under different dynamical regimes possible in the model, showing that the selective advantage to cheating can be quantified without requiring longitudinal data, analogous to signatures of selection commonly used in population genetics. This approach allows us to identify which environments allow cheats to spread, which genes are cheated across uncharacterised filamentous species, and to explore the demographic consequences of cheating for natural filamentous phage populations.
3. Jaye Sudweeks University of British Columbia
   "Environmental feedback can maintain cooperation in phages"
The evolution and maintenance of cooperation is a fundamental problem in evolutionary biology. Because cooperative behaviors impose a cost, cooperators are vulnerable to exploitation by defectors that do not pay the cost to cooperate but still benefit from the cooperation of others. Bacteriophages exhibit cooperative and defective phenotypes in infection: during replication, phages produce essential gene products in the host cell environment. Coinfection between multiple phages is possible, so if a phage cannot guarantee exclusive access to its own gene products, the products act as a public good; cooperators contribute to the common pool while defectors contribute less and instead appropriate goods from cooperators. Defective phage phenotypes experience negative frequency dependence in coinfection. For some phages, negative frequency dependence is strong enough to maintain the cooperative phenotype. For other phages, negative frequency dependence alone is not sufficient to maintain the cooperative phenotype, in which case the fate of cooperation is unclear. Here we propose that if coinfection is not enforced, and host and viral densities can vary, environmental feedback can maintain cooperation in such phage populations by modulating the rate of co-infection and shifting the advantages of cooperation versus defection. We build and analyze an ODE model and find that for a wide range of parameter values, environmental feedback maintains cooperation.
4. Nanami Kubota University of Pittsburgh
   "Cheater phages drive bacterial and phage populations to lower fitness"
How can a less reproductively fit antagonist invade a seemingly fitter population? In this study, we can partially explain such a paradox in the context of Pseudomonas phages and game theory. Most Pseudomonas aeruginosa strains carry filamentous phages called Pf that establish chronic infections and do not require host lysis to spread. However, spontaneous mutations in the Pf repressor gene (pf5r) can facilitate extreme phage production, slowing bacterial growth and increasing cell death, violating an apparent détente between bacterium and phage. Furthermore, high intracellular phage replication enables another evolutionary conflict: “cheater miniphages” lacking capsid genes invade populations of full-length phages within cells. Despite the lower absolute fitness of the pf5r bacteria, bacteria carrying both hyperactive full-length phages and miniphages outcompete the wildtype bacteria in direct competition. Surprisingly, infection by both full-length phages and miniphages can shift games between infected bacteria and naïve, uninfected cells to prisoner’s dilemma, undermining coexistence. Finally, although bacteria containing full-length phages and miniphages are most immune to superinfection by limiting the Pf receptor, this hybrid is extremely unstable, as a classic Tragedy of the Commons scenario results in complete prophage loss. The entire cycle–from phage hyperactivation to miniphage invasion to prophage loss–can occur within 24 hours, showcasing rapid coevolution between bacteria and their filamentous phages. This study demonstrates that P. aeruginosa, and potentially many other bacterial species that carry filamentous prophages, risk being exploited by Pf phages in a runaway process that reduces the fitness of both host and virus.

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

1. Thomas Hillen University of Alberta
   "Go-or-Grow Models in Biology: a Monster on a Leash"
Go-or-grow approaches represent a specific class of mathematical models used to describe populations where individuals either migrate or reproduce, but not both simultaneously. These models have a wide range of applications in biology and medicine, chiefly among those the modeling of brain cancer spread. The analysis of go-or-grow models has inspired new mathematics, and it is the purpose of this talk to highlight interesting and challenging mathematical properties. I present new general results related to the critical domain size and traveling wave problems, and I demonstrate the high level of instability inherent in go-or-grow models. We argue that there is currently no accurate numerical solver for these models, and emphasize that special care must be taken when dealing with the 'monster on a leash'' (joint work with R. Thiessen, M. Conte, T. Stepien).
2. Mark Lewis University of Victoria
   "Nonlocal Multispecies Advection-Diffusion Models"
Nonlocal advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modeling non-local advection mathematically. These often take the form of partial differential equations, with integral terms modeling the nonlocality. One common formalism is the aggregation-diffusion equation, a class of advection-diffusion models with nonlocal advection. This was originally used to model a single population but has recently been extended to the multispecies case to model the way organisms may alter their movement in the presence of coexistent species. Here we analyze behaviour in a class of nonlocal multispecies advection-diffusion models with an arbitrary number of coexisting species. We give methods for determining the qualitative structure of local minimum energy states and analyze the pattern formation potential using weakly nonlinear analysis and numerical methods. Joint work with Valeria Giunta (Swansea), Thomas Hillen (Alberta) and Jonathan Potts (Sheffield)
3. Rebecca Tyson University of British Columbia Okanagan Campus
   "The Importance of Exploration: Modelling Site-Constant Foraging"
Foraging site constancy, or repeated return to the same foraging location, is a foraging strategy used by many species to decrease uncertainty and risks. It is often unclear, however, exactly how organisms identify the foraging site. Here we are interested in the context where the actual harvesting of food is first preceded by a separate exploration period. In this context, foraging consists of three distinct steps: (1) exploration of the landscape (site-generation), (2) selection of a foraging site (site- selection), and (3) exploitation (harvesting) through repeated trips between the foraging site and ”home base”. This type of foraging has received scant attention in the modelling literature, leading to two main knowledge gaps. First, there is very little known about how organisms implement steps (1) and (2). Second, it is not known how the choice of implementation method affects the outcomes of step (3). Typical outcomes include the foragers’ rate of energy return, and the distribution of foragers on the landscape. We investigate these two gaps, using an agent-based model with bumble bees as our model organism foraging in a patchy resource landscape of crop, wildflower, and empty cells. We tested two different site-generation methods (random and circular foray exploration behaviour) and four different site-selection methods (random and optimizing based on distance from the nest, local wildflower density, or net rate of energy return) on a variety of outcomes from the site-constant harvesting step. We find that site-selection method has a high impact on crop pollination services as well as the percent of crop resources collected, while site-generation method has a high impact on the percent of time spent harvesting and the total trip time. We also find that some of the patterns we identify can be used to infer how a given real organism is identifying a foraging site. Our results underscore the importance of explicitly considering exploratory behaviour to better understand the ecological consequences of foraging dynamics. Joint work with Sarah A. MacQueen, Clara F. Hardy, and W. John Braun.
4. Chris Cosner University of Miami
   "Mean Field Games and the Ideal Free Distribution"
The ideal free distribution in ecology was introduced by Fretwell and Lucas to model the habitat selection of animal populations. It is based on the idea that individuals can assess their fitness at any location, making allowances for crowding, and will move to optimize it. In the context of the evolution of dispersal, movement strategies that can produce an ideal free distribution have been shown to be evolutionarily stable from the viewpoint of adaptive dynamics in many modeling contexts. In this paper, we revisit the ideal free distribution from the viewpoint of a habitat selection game in ecology. We specifically use the approach of mean field games, as introduced by Lasry and Lions. In that approach, an individual agent using a given strategy competes with the “mean field” of the strategies used by other agents. We find that the population density of agents converges to the ideal free distribution for the underlying habitat selection game, as cost of control tends to zero. Our analysis provides a derivation of ideal free distribution in a dynamical context.

Organized by: Daniel Cooney (University of Illinois Urbana-Champaign), Olivia Chu (Bryn Mawr College) and Alex McAvoy (University of North Carolina, Chapel Hill)

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

Note: this minisymposia has been accepted, but the abstracts have not yet been finalized.

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: Daniel Glazar (Moffitt Cancer Center & Research Institute), Renee Brady-Nicholls, Moffitt Cancer Center & Research Institute

1. Franz Kuchling Allen Discovery Center, Tufts University
   "Uncertainty Minimization as an Adaptive and Evolutionary Imperative in Biology"
Recent advances in molecular biology have enabled precise manipulation of signaling pathways in living organisms, yet a unifying framework for predicting the organismal-level emergence of form and function remains elusive. The free energy principle, originally developed for neuroscience, offers a Bayesian inference approach to model cellular decision-making during morphogenesis and emergent aneural behavior. Simulations demonstrate the utility of this framework in explaining developmental anomalies (e.g., planarian axial polarity defects) and early carcinogenesis as consequences of maladaptive cellular 'beliefs.' Complementing this, evolutionary metacognition theory formalizes adaptation across timescales, illustrating how coevolutionary processes naturally favor the emergence of multi-scale regulatory systems. These metacognitive architectures promote energy-efficient responses to fluctuating selection pressures. Experimental observations in aneural systems such as Volvox algae support these predictions: Volvox colonies display adaptive phototaxis and retain stimulus-associated behaviors beyond exposure, suggesting a primitive form of memory. These insights offer a cross-disciplinary framework—integrating developmental biology, evolutionary theory, and basal cognition—to model adaptive behavior across biological scales. This foundation may inform future directions in modeling complex diseases such as cancer, particularly where cell-state decisions and misregulation mirror maladaptive inference processes.
2. Nathanaël Hozé Université Paris Cité, INSERM, IAME, F-75018, Paris, France
   "A multi-scale modelling framework to assess the relationship between SARS-CoV-2 viral load and transmission in household studies"
Understanding the drivers of SARS-CoV-2 transmission is essential for designing effective interventions, particularly in close-contact settings such as households. While viral load is widely believed to influence infectiousness, quantifying its role remains challenging due to individual variability, asymptomatic infections, and the unobservability of transmission events. Household studies offer a controlled context for investigating the link between viral load dynamics and transmission, especially when combined with high-frequency sampling. However, such designs are costly, and their added value relative to simpler approaches is unclear. We present a multi-scale modelling framework that integrates within-host viral dynamics and between-host transmission processes in household settings. We developed a stochastic agent-based model of viral dynamics that includes inter-individual variability. We developed a Bayesian inference approach implemented in rstan, in which we jointly estimate individual-level parameters, infection times, and the relation between viral load and transmissibilty. Our simulation-based framework evaluates whether monitoring viral load at high temporal resolution improves the reconstruction of transmission chains and the estimation of key epidemiological parameters. We compare this rich sampling design to two more commonly used alternatives: (i) designs based solely on symptom onset, and (ii) designs based on qualitative viral detection (i.e., positive/negative status without quantification). We show that incorporating quantitative viral load data improves the accuracy of transmission chain reconstruction and enhances the estimation of key metrics, including the probability of infection, generation interval, and incubation period. This work provides quantitative insights into the potential benefits of incorporating viral load measurements into household transmission studies and informs the design of future studies aimed at elucidating the role of viral kinetics in infectious disease spread.
3. Kathleen Wilkie Toronto Metropolitan University
   "Practical Parameter Identifiability and Handling of Censored Data with Bayesian Inference in Models of Tumour Growth"
Mechanistic mathematical models are a powerful tool to help us understand and predict the dynamics of tumour growth under various conditions. In this work, we use five models with an increasing number of parameters to explore how certain (often overlooked) decisions in estimating parameters from data affect the outcome of the analysis. In particular, we propose a framework for including tumour volume measurements that fall outside the upper and lower limits of detection, which are normally discarded. We demonstrate how excluding censored data results in an overestimation of the initial tumour volume and the model-predicted tumour volumes prior to the first measurements, and an underestimation of the carrying capacity and the predicted volumes beyond the latest measurable time points. We show how the choice of prior for the model parameters can impact the posterior distributions, and illustrate that reporting the most likely parameters and their 95% credible interval can lead to confusing or misleading interpretations. We hope this work will encourage others to carefully consider the choices made in parameter estimation and to consider adopting the approaches discussed in this talk.
4. Ernesto A. B. F. Lima The University of Texas at Austin
   "Modeling tumor sensitivity and resistance: a bayesian framework for predicting combination therapies"
Understanding the heterogeneous response of tumors to therapy remains a major challenge in oncology, particularly in the presence of treatment resistance. We present a framework to model the growth dynamics of radiation-sensitive and radiation-resistant breast cancer cells receiving radiotherapy, immunotherapy, and their combination. Using experimental data from murine models, we construct a family of ordinary differential equation models and apply Bayesian calibration and model selection to identify the most parsimonious model capable of capturing and predicting the observed experimental dynamics. Our approach quantifies differences between sensitive and resistant tumors. Resistant cells exhibited not only faster intrinsic growth rates but also a greater capacity for post-radiotherapy repair compared to sensitive cells. These biological differences were incorporated into the modeling through group-specific parameters, selected using the Bayesian Information Criterion to balance model complexity and predictive ability. In the immunotherapy arm, a pronounced heterogeneity in treatment response was observed. By performing mouse-specific calibration of key parameters governing immunotherapy efficacy and linking them to imaging-derived biomarkers, we successfully captured this variability across subjects. For the combination therapy predictions, the concordance correlation coefficient and Pearson correlation coefficient increased from 0.31 and 0.34 (without biomarkers) to 0.34 and 0.54 (with biomarkers), demonstrating the added predictive value of imaging-informed modeling. The Bayesian framework enabled robust parameter estimation, uncertainty quantification, and assessment of model identifiability, providing insights into the dynamics of combination therapy. Our results emphasize the importance of accounting for intra-tumoral heterogeneity in predictive modeling to improve treatment planning and evaluation.

Organized by: Jennifer Flegg (University of Melbourne), Prof Mat Simpson, Queensland University of Technology

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

1. Ruth Baker University of Oxford
   "Optimal experimental design for parameter estimation in the presence of observation noise"
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, in particular in fields such as biology and ecology. In this context, accurate parameter estimation is crucial; model parameters are used to both quantify observed behaviour, characterise behaviours that cannot be directly measured and make quantitative predictions. The extent to which parameter estimates are constrained by the quality and quantity of available data is known as parameter identifiability, and it is widely understood that for many dynamical models the uncertainty in parameter estimates can vary over orders of magnitude as the time points at which data are collected are varied. In this talk I will outline recent research that uses both local and global sensitivity measures within an optimisation algorithm to determine the observation times that give rise to the lowest uncertainty in parameter estimates. Applying the framework to models in which the observation noise is both correlated and uncorrelated demonstrates that correlations in observation noise can significantly impact the optimal time points for observing a system, and highlights that proper consideration of observation noise should be a crucial part of the experimental design process.
2. Yong See Foo University of Melbourne
   "Quantifying structural uncertainty in chemical reaction network inference"
Dynamical systems in biochemistry are complex, and one often does not have comprehensive knowledge about the interactions involved. Chemical reaction network (CRN) inference aims to identify, from observing species concentrations, the unknown reactions between the species. Most approaches focus on identifying a single, most likely CRN, without addressing uncertainty about the resulting network structure. However, it is important to quantify structural uncertainty to have confidence in our inference and predictions. To this end, I will discuss how to construct posterior distributions over CRN structures. This is done by keeping a large set of suboptimal solutions found in an optimisation framework with sparse regularisation, in contrast to existing optimisation approaches which discard suboptimal solutions. I will show that inducing reaction sparsity with nonconvex penalty functions results in more parsimonious CRNs compared to the popular lasso regularisation. In a real-data example where multiple CRNs have been previously proposed, reactions proposed from different literature can be simultaneously recovered under structural uncertainty. Moreover, posterior correlations between reactions help identify where structural ambiguities are present. This can be translated into alternative reaction pathways suggested by the available data, which guide the efforts of future experimental design.
3. Michael Pan The University of Melbourne
   "Thermodynamic modelling of membrane transport processes using bond graphs"
Cellular systems are physical systems, and are therefore governed by the laws of physics and thermodynamics. Energy is fundamental to our understanding of membrane transporters, which will only operate in the direction of decreasing chemical potential. Despite this, energy is often ignored in mathematical models of transporters, leading to unrealistic behaviours analogous to perpetual motion machines. In this talk, we outline a general physics-based framework (the bond graph) that explicitly models energy and therefore inherently accounts for thermodynamic constraints in membrane transporters. We show that this framework also provides a natural means of modelling the voltage dependence of electrogenic transporters. We demonstrate the utility of the bond graph approach in modelling the cardiac Na+/K+ ATPase (sodium-potassium pump) and discuss potential extensions of this approach for whole-cell modelling.
4. Jean (Jiayu) Wen The Australian National University
   "Advancing Genomic Foundation Models with Electra-Style Pretraining: Efficient and Interpretable Insights into Gene Regulation"
Pre-training large language models on genomic sequences has emerged as a powerful strategy for capturing biologically meaningful representations. While masked language modeling (MLM)-based methods, such as DNABERT and Nucleotide Transformer, achieve strong performance, they are hindered by inefficiencies due to partial token supervision and high computational demands. To address these limitations, we introduce the first Electra-style pretraining framework for genomic foundation models, replacing the MLM objective with a replaced-token detection task that employs a discriminator network to distinguish tokens replaced by a generator, enabling dense token-level supervision and significantly accelerating training. Unlike conventional methods that tokenize genomic sequences into 6-mers, our model operates at single nucleotide resolution, enhancing both efficiency and interpretability. We pre-train our model on the human genome and fine-tune it across a spectrum of downstream genomic prediction tasks, spanning epigenetics, transcriptional regulation, and post-transcriptional processes, including identification of regulatory elements such as promoters and enhancers, prediction of histone modifications, assessment of chromatin accessibility, as well as prediction of RNA-protein interactions, RNA modifications, RNA stability, translational efficiency, and microRNA binding sites. By addressing these diverse tasks, our model contributes to the advancement of whole cell modeling, which requires an integrated understanding of genomic, transcriptomic, and proteomic interactions. Our approach achieves a 28-fold reduction in pretraining time compared to MLM-based methods while surpassing their performance in most downstream evaluations, with benchmarking against state-of-the-art genomic models. Comprehensive ablation studies illuminate the key factors driving this improved efficiency and effectiveness. Furthermore, the use of 1-mer tokenization allows for nucleotide-level resolution, greatly enhancing the model's interpretability, with visualization and attention analyses demonstrating its ability to capture biologically relevant sequence motifs at a fine-grained level, providing deeper insights into genomic regulatory mechanisms. This work underscores the potential of Electra-style pretraining as a computationally efficient and effective strategy for advancing genomic representation learning, with broad implications for systems biology and whole cell modeling.

Organized by: Kelsey Gasior (University of Notre Dame)

1. Samuel Oliver Swansea University
   "The role of EMT in Ovarian Cancer: Insights from a Mathematical Model"
The role of EMT in Ovarian Cancer: Insights from a Mathematical Model Epithelial-to-mesenchymal transition (EMT) is a critical process in cancer progression that can significantly reduce the effectiveness of treatments. EMT occurs when cells undergo phenotypic changes, resulting in altered behaviours compared to their original state. This transition may lead to increased drug resistance, greater cell plasticity, and enhanced metastatic potential. As a result, understanding and studying the role of EMT in tumour progression and treatment response is essential. In this study, we utilise a 3D agent-based multiscale modelling framework with PhysiCell to examine the role of EMT over time in two ovarian cancer cell lines, OVCAR-3 and SKOV-3. This approach enables us to investigate the spatiotemporal dynamics of ovarian cancer and provide insights into the development of the tumours. The model incorporates microenvironmental conditions, adjusting cellular behaviours based on factors such as substrate concentrations and the proximity of neighbouring cells. The OVCAR-3 and SKOV-3 cell lines exhibit significantly different tumour architectures, allowing for the exploration of various tumour dynamics and morphologies. The model successfully captures biological patterns observed in tumour growth and progression, offering valuable insights into the dynamics of these cell lines. Additionally, sensitivity analysis is conducted to evaluate the impact of parameter variations on model outcomes.
2. Nate Kornetzke University of New Mexico
   "Turn down that noise! Uncertainty quantification for stochastic models of emerging infectious pathogens"
Emerging infectious pathogens are a persistent public health threat that challenge traditional mechanistic modeling approaches. As outbreaks initially start with a low number of infected hosts, the dynamics of these outbreaks are highly stochastic, making traditional deterministic methods, e.g. ordinary differential equations, unable to qualitatively or quantitatively capture the transmission dynamics. Instead, stochastic models are used, such as Markov chain models, but these models present their own challenges. Often, to infer a quantity of interest with these stochastic models, we need to sample the model’s distribution many times over, introducing an additional source of noise to our analysis. This additional noise can be amplified around bifurcating points of the model, making the inference of our quantity of interest even more difficult. Here, we show how novel tools from the field of uncertainty quantification can be used to disentangle noise in stochastic systems to make rigorous statistical inferences that are crucial for modeling emerging pathogens. We illustrate these techniques with a model of yellow fever virus spillover in the Americas, a virus that has seen rapid emergence amongst multiple hosts and vectors in South America over the last decade.
3. Steve Williams University of California, Merced
   "Examining models of phenotype selection in populations of bacteria under external predatory stress"
Biofilms are dense communities of bacteria living in a collective extracellular matrix. They aid their constituent bacteria by protecting them from external environmental threats, distributing metabolic workload, and performing complex multicellular processes (e.g., quorum sensing). However, for many organisms, retaining the tools necessary to be multiple phenotypes within their lifetime has been essential for survival. It is natural to wonder how external stressors in marine environments can impact the biofilm formation process and whether these impacts have downstream implications for their participation in multi-organism relationships. To explore this adaptation process, we have employed a previously proposed population model in which bacteria transition freely between planktonic and biofilm phenotypes in the presence of predator. By employing several sensitivity analysis techniques, we probe the parameter space to understand the impacts that changing bacterial dynamics can have. Using synthetic data, we have quantified uncertainties present in the realization of our system using practical identifiability techniques. Finally, we propose a new model with parameter variations within the bacterial population, particularly their ability to attach to biofilms. Through the lens of sensitivity analysis again, this model allows us to begin to measure the rate of adaptation for such populations in terms of the size of the external stressors and the distribution of the variation inside the population.
4. Kelsey Gasior University of Notre Dame
   "Comparative Sensitivity Analyses and Modeling the Epithelial Mesenchymal Transition"
The epithelial mesenchymal transition (EMT) is a process that allows carcinoma cells to lose their adhesivity and migrate away from a tumor. Further, cells can maintain this invasiveness after they leave their original microenvironment, suggesting that there is an underlying bistable switch. We developed a mathematical model that examined the relationships between E-cadherin and Slug and their responses to tumor-level factors, such as cell-cell contact and TGF-b. Phenomenological model behavior was derived from biological experiments and, ultimately, this model showed how cells at different positions within a tumor can use exogenous factors to undergo EMT. However, the nonlinear dynamics and estimated model parameters make it challenging to analyze and understand what parameters contribute to the observed E-cadherin and Slug changes. Thus, we turn to sensitivity analysis. This work seeks to understand the true impact of mathematical and statistical techniques on our understanding of the dynamics underlying EMT. To provide an extensive understanding, multiple ranges were examined for each parameter and techniques such as nondimensionalization, Latin Hypercube Sampling, Partial Rank Correlation Coefficient, Morris Method Screening, and Sobol’ analysis were used. This wide range of techniques was applied to cells exposed to different levels of cell-cell contact and exogenous TGF-b. By comparing these different methodologies, parameter ranges, and treatment groups, a dual biological and mathematical perspectives emerge. While the different analytical techniques highlight different parameters of importance and interacting relationships, comparing across treatment groups shows how a cell’s identity can be controlled by different intracellular factors, which may shift in the dynamic tumor environment. Together, these results highlight the need for extensive and methodical approach to sensitivity analysis before conclusions can be reached to inform future experiments.

Organized by: Jinsu Kim (POSTECH), Eric Foxall (The University of British Columbia - Okanagan Campus), and Linh Huynh (Dartmouth College)

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

1. Jinsu Kim POSTECH
   "Stability of stochastic biochemical reaction networks"
A reaction network is a graphical representation of interactions between chemical species (molecules). When the species' abundances in the system are low, the inherent randomness of molecular interactions significantly influences the system dynamics. In such cases, the abundances are modeled stochastically using a continuous-time Markov chain that evolves in a jump-by-jump fashion. A major challenge in this area is establishing the stability of the Markov chain—that is, proving the existence of a stationary distribution. Another goal is to find a closed form of the stationary distribution, which is often extremely difficult. In this talk, I will present structural conditions on reaction networks that guarantee stability. I will also introduce novel techniques, inspired by reaction network theory, that aid in deriving closed-form expressions for stationary distributions.
2. Daniel Schultz Dartmouth College
   "Emergence of heterogeneity during bacterial antibiotic responses"
Heterogeneity is a fundamental aspect of microbial ecology, conferring resilience and adaptability to microbial populations. Remarkably, this heterogeneity does not necessarily depend on complex mechanisms of differentiation into specialized phenotypes but can instead be achieved through fundamental processes that are common to all microbes. Yet, despite significant advances in describing microbial physiology, we still lack a framework to bridge across scales to connect cellular processes to emergent behaviors in microbial communities. Here, we aim to understand how stochastic and spatial variations affect cellular metabolism and thereby provide a mechanism to generate phenotypic diversity, giving rise to complex collective behaviors in microbial populations. To overcome difficulties in studying cell responses across multiple scales, we use single-cell and biofilm microfluidics to develop mathematical models of antibiotic response dynamics. Our single-cell microfluidic experiments capture a remarkable variety of phenotypes caused by stochastic fluctuations during drug responses. Similarly, our model predicts the coexistence of stable phenotypes corresponding to growing and arrested cells. We describe the nature and stability of these different phenotypes and connect single-cell heterogeneity to population-level growth. In our biofilm microfluidic experiments, the formation of nutrient gradients due to spatial variations across the population results in a range of metabolic states with different antibiotic susceptibilities. Drug exposures result in a major reorganization of the biofilm, giving rise to collective behaviors such as increased resistance and “memory” from past exposures. A spatial version of our model describes the contribution of spatial structure to the collective mechanisms of resistance provided by organization into biofilms, showing how spatially structured populations can survive much higher drug doses than planktonic populations. Together, these results elucidate how heterogeneity emerges in microbial populations and how it gives rise to complex behaviors at the population level.
3. Anna Kraut St. Olaf College
   "Evolution across fitness valleys in a changing environment"
The biological theory of adaptive dynamics aims to study the interplay between ecology and evolution under the basic mechanisms of heredity, mutation, and competition. The typical evolutionary behavior of a population can be studied mathematically by looking at macroscopic limits of large populations and rare mutations derived from microscopic individual-based Markov processes. Previous work has been focused on a variety of scaling regimes and the resulting stochastic and deterministic limit processes under the assumption of constant environmental parameters. In our present work, we relax this assumption and study repeating changes in the environment, allowing for all of the model parameters to vary over time as periodic functions on an intermediate time scale between those of stabilization of the resident population (fast) and exponential growth of mutants (slow). Biologically, this can for example be interpreted as the influence of seasons or the fluctuation of drug concentration during medical treatment. Analyzing the influence of the changing environment carefully on each time scale, we are able to determine the effective growth rates of emergent mutants and their invasion of the resident population. In recent work, we study the crossing of so-called fitness valleys, where multiple disadvantageous mutations need to be accumulated to gain a fitness advantage. A changing environment has interesting implications for the crossing rates of such valleys, particularly if some of the intermediate traits occasionally have positive growth rates and can serve as pit stops.
4. Eric Foxall UBC Okanagan
   "Perturbation theory of reproductive value for branching Markov processes"
The reproductive value gives an individual’s relative contribution to the success of a population, as a function of its type, and for suitably recurrent models can be computed via a renewal argument. We show that the same argument can be used to compute its sensitivity in terms of an associated Markov process that describes the trajectory of a distinguished lineage, known to probabilists as the spinal particle. In the case of age-structured models this leads to nice formulas for the dependence of reproductive value on parameters.

Organized by: Tomas Helikar (University of Nebraska - Lincoln), Juilee Thakar (Juilee_Thakar@URMC.Rochester.edu) - University of Rochester Medical Center James Glazier (jaglazier@gmail.com) - Indiana University

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

1. Gary An University of Vermont
   "NASEM-compliant Critical Illness Digital Twins to cure sepsis"
To date there are no pharmacological agents that can substantively and reliably affect the underlying host pathophysiology of sepsis. The effective control of sepsis requires personalized precision medicine, which requires the capabilities provided by digital twins compliant with industrial standards and consistent with the definition put forth in the National Academies of Science, Engineering and Medicine (NASEM) report entitled 'Foundational Research Gaps and Future Directions for Digital Twins' that provides an operational definition for a digital twin and lists specific challenges moving forward for the development of this technology. NASEM defines a digital twin thusly: 'The key elements that comprise a digital twin include (1) modeling and simulation to create a virtual representation of a physical counterpart, and (2) a bidirectional interaction between the virtual and the physical. This bidirectional interaction forms a feedback loop that comprises dynamic data-driven model updating (e.g., sensor fusion, inversion, data assimilation) and optimal decision-making (e.g., control, sensor steering).' Notably, this definition is not met by the vast majority of currently described biomedical “digital twins,” and this insufficiency limits the applicability of non-NASEM compliant digital twins to provide the true personalized precision medicine required to treat complex immune diseases such as sepsis. We present a prototype Critical Illness Digital Twin developed with a workflow that utilizes mechanistic models with machine learning and artificial intelligence for clinically relevant parameter space identification, trajectory personalization, discovery of novel multimodal/adaptive therapeutic control and guidance for sensor/actuator development. The CIDT is based on a previously validated agent-based model of systemic inflammation, and constructed to conform to a mathematical object terms the Model Rule Matrix (MRM). The MRM employs the Maximal Entropy Principle to account for the latent space of 'what is left out' (e.g. Epistemic Uncertainty) in the rule structure of the CIDT. Operating on the CIDT with a workflow that includes genetic algorithms and active learning we identified non-falsifiable configurations of the MRM with respect to two distinct clinical cytokine time-series datasets, one for burns, one for trauma. We further applied deep reinforcement learning to train an artificial intelligence that can cure sepsis arising from a novel pathogen by modulating host cytokines using only currently FDA-approved biologics. Additional future work must include testing with a sufficiently complex large animal model that can recapitulate the heterogeneity seen in clinical sepsis.
2. Yi Jiang Georgia State University
   "Immunogenic Cell Death: The Key to Unlocking the Potential for Combined Radiation and Immunotherapy"
Immunogenic cell death (ICD) enhances anti-tumor immunity by releasing tumor-associated antigens and activating the anti-tumor immune system response. Here, we develop a mathe- matical model to quantify the role of ICD in optimizing the efficacy of combined radiotherapy (RT) and macrophage-based immunotherapy. Using preclinical murine data targeting the SIRPα-CD47 checkpoint, we show that RT alone induces minimal ICD, whereas disrupting the SIRPα-CD47 axis significantly enhances both phagocytosis and systemic immune activation. Our model predicts an optimal RT dose (6–8 Gy) for maximizing ICD, a dose-dependent abscopal effect, and a hierarchy of treatment efficacy, with SIRPα-knockout macrophages exhibiting the strongest tumoricidal activity. These findings provide a quantitative framework for designing more effective combination therapies, leveraging ICD to enhance immune checkpoint inhibition and radiotherapy synergy.
3. Hana Dobrovolny Texas Christian University
   "Incorporating the immune response into models of oncolytic virus treatment of cancer"
Oncolytic viruses present a promising path for cancer treatment due to their selectivity in infecting and lysing tumor cells and their ability to stimulate the immune response. While the immune response can help eliminate the tumor, it also acts to clear the virus and often limits the effectiveness of oncolytic virus therapy. Using experimental data, we test models of oncolytic virus infections incorporating various immune components in order to determine the most suitable immune models. We use the models to investigate the role of the immune response in oncolytic virus treatment, finding that a moderate immune response can prolong the oncolytic virus infection, allowing the virus to infect and kill more tumor cells than either a weak or strong immune response.
4. Jason E. Shoemaker University of Pittsburgh
   "Network representation of sex-specific immunity: A steppingstone to digital twins?"
In a world of immense and growing computational power, the eventual rise of Digital Twins will enable a degree of personal health optimization that is currently unimaginable. There are important questions on how society gets there, the ethics of owning one’s digital twin, and many more important questions to address as we progress towards the Digital Twin world. One small but important question in the short term is how we can use currently available tools to design personal treatments today or guide drug discovery. In our lab, we have leaned heavily on using molecular interaction networks as baseline models of human gene regulation. We have both independently and with colleagues developed new algorithms that can integrate interaction data and gene expression data to predict either drug mechanisms of action or pathways for suppressing respiratory virus replication. Now, we are using these tools to explore for antiviral drug targets that are sex-specific, meaning proteins that, when targeted, may help regulate virus replication specially in male or females. And we are extending these studies to determine what roles hormones may play as well. Here, we will discuss our early results wherein we have analyzed primary human nasal cells from male and female donors. Our early results show that network-based representations of gene regulation better isolate hormone regulated pathways, including inflammation pathways important to respiratory infection. With sufficient data, network-based approaches combined with machine learning may be a promising approach developing early digital twins that are relevant to respiratory infection.

Organized by: Hannah Anderson (Moffitt Cancer Center), Kasia Rejniak, Moffitt Cancer Center

1. Hannah Anderson Moffitt Cancer Center
   "Evaluating robustness of an optimized regimen in a virtual murine cohort of bladder cancer"
Virtual cohorts can capture the heterogeneity across patient populations and thus different responses to treatment. In this talk, we develop an ODE model of a combination therapy for mice implanted with bladder cancer. Using a murine data set, we develop a virtual cohort using a framework that consists of 1) structural identifiability, 2) modifying data use, 3) estimating parameters, 4) determining practically identifiable parameters, 5) obtaining parameter distributions, and then 6) simulating the virtual cohort alongside data. Using the parameter set that represents an average mouse from data, we perform optimal control to optimize a regimen for adoptive cell therapy in combination with gemcitabine. Then, we evaluate the robustness of this regimen by determining its efficacy when applied to the virtual murine cohort.
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. Xinyue Zhao University of Tennessee Knoxville
   "Optimal control of free boundary models for tumor growth"
In this talk, we will investigate the optimal control of treatment in free boundary PDE models for tumor growth. The optimal control strategy is designed to inhibit tumor growth while minimizing side effects. In order to characterize it, the optimality system is derived, and a necessary condition is obtained. Numerical simulations will be presented to illustrate the theoretical findings and assess the impact of the optimal control strategy on tumor growth dynamics.
4. Luis Maria Lopes da Fonseca University of Florida
   "Surrogate modeling and control of medical digital twins"
The vision of personalized medicine is to identify interventions that maintain or restore a person's health based on their individual biology. Medical digital twins, computational models that integrate a wide range of health-related data about a person and can be dynamically updated, are a key technology that can help guide medical decisions. Such medical digital twin models can be high-dimensional, multi-scale, and stochastic. To be practical for healthcare applications, they often need to be simplified into low-dimensional surrogate models that can be used for the optimal design of interventions. Here, we introduce surrogate modeling algorithms for optimal control applications. As a use case, we focus on agent-based models (ABMs), a common model type in biomedicine for which there are no readily available optimal control algorithms. By deriving surrogate models based on systems of ordinary differential equations, we show how optimal control methods can be employed to compute effective interventions, which can then be lifted back to a given ABM. The relevance of the methods introduced here extends beyond medical digital twins to other complex dynamical systems.

Organized by: Veronica Ciocanel (Duke University), Hye-Won Kang, University of Maryland Baltimore County

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

1. Grzegorz Rempala The Ohio State University
   "Modeling Epidemics on Networks"
This talk presents an overview of recent advances in modeling epidemic dynamics on networks, with a focus on pairwise and edge-based formulations of SIR-type processes on random graphs. I will outline a systematic framework for deriving and analyzing models across multiple levels of complexity, emphasizing the role of closure and approximation techniques. Particular attention will be given to conditions under which models become exact or analytically tractable, and to clarifying how commonly used heuristic models relate to their rigorous mathematical foundations.
2. Paul Hurtado University of Nevada, Reno
   "SIER-type ODE models with phase-type latent and infectious period distributions"
SEIR-type ODE models can be viewed as a mean-field model corresponding to (often unspecified) individual-based stochastic model. These typically assume that the latent and infectious periods follow exponential distributions, or Erlang (gamma) distributions, if formulated using the linear chain trick (LCT). SEIR models based on the generalized linear chain trick (GLCT) expand these assumptions to possibly include the much broader class of 'phase-type' distributions, which can be thought of as the absorption time distributions for finite-state Continuous Time Markov Chains. These include Coxian distributions, hypoexponential (generalized Erlang) distributions, and mixtures of these distributions. In this talk, I will present some preliminary explorations of how SEIR-type model behaviors change when we replace those traditional (exponential or Erlang) distribution assumptions for the latent and infectious period distributions with these more flexible alternatives. I'll also discuss implications for the empirical estimation of these distributions in applications.
3. Deena Schmidt University of Nevada, Reno
   "Modeling network formation in ecological systems"
Understanding how networks form and evolve is an important question in many fields such as ecology, epidemiology, economics, and sociology. Studying the mechanisms of network formation can yield insights into which factors are involved in edge formation and network growth. In this talk, I will give an overview of network formation models and then focus on such modeling in ecological systems, specifically thinking about caterpillar-plant interaction networks using data collected from Ecuador. I will discuss two modeling frameworks, the repeated choice model (RCM) and the stochastic actor-oriented model (SAOM). The RCM models network formation as a series of choices, where caterpillars select plants based on observable features such as leaf count. The SAOM focuses on the stochastic choices individuals make and how their choices are influenced by the network structure as well as their own attributes. I will present some preliminary results for the Ecuador interaction networks. This is work in progress with graduate student Andrew Chavez.
4. Wenrui Hao Pennsylvania State University
   "A Systematic Computational Framework for Practical Identifiability Analysis"
Practical identifiability is a fundamental challenge in data-driven modeling of mathematical systems. In this talk, I will present our recent work on a novel framework for practical identifiability analysis, designed to assess parameter identifiability in mathematical models of biological systems. I will begin with a rigorous mathematical definition of practical identifiability and establish its equivalence to the invertibility of the Fisher Information Matrix. Our framework connects practical identifiability with coordinate identifiability, introducing a novel metric that simplifies and accelerates parameter identifiability evaluation compared to the profile likelihood method. Additionally, we incorporate new regularization terms to address non-identifiable parameters, enhancing uncertainty quantification and improving model reliability. To support experimental design, we propose an optimal data collection algorithm that ensures all model parameters are practically identifiable. Applications to Hill functions, neural networks, and dynamic biological models illustrate the framework’s effectiveness in uncovering critical biological processes and identifying key observable variables.