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-3, and Part-4.

1. Ishraq U Ahmed University of Sydney
   "Free cholesterol toxicity and impaired cell recycling in a lipid-structured model of atherosclerosis"
The resolution of chronic inflammation involves a dynamic balance between cell death and the clearance of dying cells via efferocytosis. In nonresolving atherosclerotic plaques, this balance is disrupted due to the accumulation of high levels of intracellular cholesterol. Cholesterol is initially stored within the cell in the form of cholesterol esters, but some of this is hydrolysed to form free cholesterol. Excess free cholesterol is cytotoxic to macrophages, and impairs their efferocytic ability and promotes necrotic cell death. In nonresolving plaques, the impairment of cellular function and increase in cell death rates can lead to the formation of a necrotic core. In this talk, we present a preliminary partial integro-differential equation model for the early development of atherosclerotic tissue, where the cell population is structured by cholesterol content. Cells can accumulate cholesterol by ingesting it from LDL or dead cells, and can reduce their cholesterol load by proliferating. The model includes cell death via both apoptosis and necrosis, where necrotic material is ingested by live cells more slowly than apoptotic material. Death rates themselves depend on the levels of esterified and free cholesterol, where the relative levels of each are obtained from a coupled single-cell ODE model that describes intracellular cholesterol processing. With this model, we study how free cholesterol-induced cell death can lead to full tissue necrosis if efferocytosis rates are insufficient. We also consider how cell proliferation can help mitigate tissue necrosis by lowering intracellular cholesterol loads.
2. Pak-Wing Fok University of Delaware
   "Impact of Medial Calcification on Arterial Mechanics and Hemodynamics"
Medial Arterial Calcification (MAC) often occurs in aging arteries, promoted by diabetes mellitus and chronic kidney disease. Advanced MAC represents a frequent cause of chronic limb-threatening ischemia and limb amputation. Through a 1D haemodynamics simulation, we study how the mechanical properties of calcified arterial tissue and hydraulic resistance in the peripheral circulation jointly impact hemodynamics as MAC develops. We find that (i) there is a greater drop in systolic pressure across calcified arteries compared to healthy arteries, but this drop can be offset by greater peripheral resistance, provided left ventricular function is intact, (ii) both calcification and enhanced peripheral resistance lead to reduced flow rates, reduced peripheral perfusion, and peripheral tissue hypoxemia and (iii) pressurized calcified arteries present lumen areas that are smaller compared to healthy arteries, even though they are larger when unpressurized. Our simulations suggest that the increased impedance in calcified arteries results from smaller in-vivo lumen areas. This can reduce the outflow rate, but the effect is complicated by arteriole closures, vessel geometry, and global pressure. These findings confirm previously reported observations of flow reduction in calcified arteries.
3. Laura Ellwein Fix Virginia Commonwealth University
   "A closed-loop system-level model of cerebrovascular reactivity"
Cerebrovascular reactivity (CVR) is a metric of the ability of cerebral blood vessel tone to respond to stimuli for regulating blood flow and metabolism in the brain. In one such mechanism, the cerebrovasculature dilates to lower resistance in response to increased arterial carbon dioxide (CO2), thereby increasing blood flow to wash out the CO2. However, the integration of this with other processes and the implications for the systemic circulation are still not fully understood. Previously, Ellwein et al. developed a closed-loop system-level circulation model, in which cerebrovascular resistance was modeled using a piecewise linear function parameterized empirically using available data for blood flow velocity in the middle cerebral artery, arterial blood pressure, and expired CO2. In the current work we replaced the piecewise linear function with a more mechanistic representation of cerebral resistance as a function of partial pressure of CO2 together with a first-order control equation. Initial model simulated dynamics compare well to those previously achieved by Ellwein et al., with improved physiological fidelity. We also incorporated systemic responses to CO2 and optimized model parameters against a new cohort of data obtained under CO2 rebreathing conditions. These model adaptations will improve understanding of the system-level integration of mechanisms behind CBF regulation and CVR.
4. Liam Murray The University of Melbourne
   "Myofibril networks produce shear stress in sheep cardiomyocytes"
Myofibril arrangement is critical to cardiac muscle function in health, exercise, and disease. Historically, analysis of myofibril organisation impact on force and cell contraction has relied on the assumption of parallel, longitudinal arrays. However, improvements in imaging indicate that myofibrils may form complex networks. How these anisotropic networks modulate cell-contraction and force has yet to be explored. Here, morphological analysis of sheep cardiomyocytes has informed finite element models of cell contraction. Analysis of U-NET++ segmentations of Z-Discs demonstrate that myofibrils have a distribution of orientation throughout the cell. Simulations have similarly produced unique deformation patterns for geometries informed by myofibril orientations. These patterns highlight the physiological impact of myofibril structure and update understanding of uniaxial contraction to consider shear stress.

Organized by: Hermann Eberl (University of Guelph), John Ward

1. John P. Ward Loughborough University
   "An analysis of large time solutions in biofilm models of Wanner-Gujer type"
The Wanner-Gujer model has a long history in the modelling of biofilm growth, providing a framework to investigate spatio-temporal homogeneities of bacterial biofilm growth and structure in response to environmental factors. Nearly all applications of the model involve numerical solutions or a mathematical analysis (existence and uniqueness) of the time-dependent problem. However, in many applications the steady-state scenario is of most interest, as biofilms in bioreactors are required to run for several weeks or months. In this talk we present a systematic approach to the analysis of the long-time solutions of Wanner-Gujer type models, in particular travelling wave solutions (representing growth on an intermediate timescale) and steady-state solutions (in the case of material sloughing). Numerical solutions of these limiting cases enables an efficient exploration across parameter space and a  means of deriving parameter sets to optimise certain desirable properties (e.g. speed of growth, biofilm thickness etc.). A few illustrative examples will be presented.
2. Rachana Mandal University of Guelph
   "Modeling and Simulation of Biofilm Growth in a Counter-Diffusion System, Coupled with Biozone Formation in the Aqueous Phase by Chemotactic Bacteria"
In marine environments, sessile bacteria in biofilms and planktonic bacteria suspended in the aqueous medium, critically influence nutrient fluxes, particularly around plumes of marine snow that serve as moving nutrient hotspots. We develop a mathematical model on bacterial biofilm study that accounts for biomass growth, surface attachment and detachment, and chemotactic-diffusive movement of planktonic bacteria and perform a numerical simulation study. The biomass density controls the spatial expansion of biofilm, whereas biomass growth depends on the concentration of the substrates, such as carbon, an electron donor, and oxygen, an electron acceptor. Carbon, sourced from marine snow, diffuses into the domain from one boundary, while oxygen enters from the opposite boundary, establishing a counter-diffusion system. Under these conditions, chemotactic planktonic bacteria accumulate in regions with favorable growth conditions. The system is described by a one-dimensional set of four highly nonlinear partial differential equations. The flux-conservative finite volume method is used for space discretization of the transport terms corresponding to the biomass in biofilm and suspension. Later the substrate equations are discretized and numerically solved using the time-adaptive method from ‘ReacTran’ library in ‘R’. Simulation results demonstrate biofilm expansion toward the aqueous phase and the dynamic migration of suspended bacteria toward optimal nutrient zones. The interplay between chemotaxis, attachment, detachment, and counter-diffusion is shown to significantly influence biofilm maturation dynamics.
3. Blessing Emerenini Rochester Institute of Technology
   "Modeling Biofilm Induced Corrosion Inhibition - what do we know?"
Corrosion mitigation represents a significant scientific and engineering challenge, with associated costs exceeding half a trillion dollars annually in the United States alone. Advancing corrosion prevention and control strategies is essential for enhancing the resilience and sustainability of civil infrastructure. Emerging evidence highlights the critical role of naturally occurring microbial biofilms, particularly through a phenomenon known as microbially induced corrosion inhibition (MICI), where biofilms on metal surfaces can reduce or slow corrosion processes. Developing an effective and reliable MICI-based biotechnologies requires an integrated approach, and comes with questions on sustainability. In this study, we investigate a range of modeling frameworks to identify and optimize key parameters influencing the long-term sustainability of such technologies.
4. Maria Rosaria Mattei University of Naples Federico II
   "A modeling and simulation study of horizontal gene transfer in biofilms"
The global spread of Antibiotic Resistance Genes (ARGs) and Metal Resistance Genes (MRGs) represents an increasing health concern, and has been mainly attributed to antibiotics abuse and misuse. Dissemination of ARGs and MRGs is largely associated to plasmids, extra-chromosomal genetic elements. Plasmid-carried resistance is transferred to new host cells through Horizontal Gene Transfer (HGT) mechanisms, which play a crucial role in the ecological success of plasmids in bacterial communities. HGT occurs through three main mechanisms, namely conjugation, transformation and transduction, the latter referring to the case where foreign DNA is acquired by the recipient bacterium through infection by bacteriophages. In this talk, we present a biofilm model formulated as a Wanner-Gujer type free-boundary problem describing the impact of HGT on plasmid spread in biofilm communities. Nonlinear hyperbolic PDEs govern the advective transport and growth of the solid-phase components constituting the biofilm, while parabolic quasilinear PDEs model the diffusion-reaction of soluble substrates and bacteriophages. Conjugation is modelled as a mass-action kinetics process subsequent to gene expression, modelled as a nonlocal term to account for recipient-sensing mechanisms. Natural transformation is modelled as a frequency-dependent process. The presence of transducing phages is included in the model and their production is considered as a deterministic process resulting from the infection by lytic phages of bacterial cells carrying the plasmid. We investigate through numerical simulations the comparative influence of conjugation and transformation on the spread of antibiotic resistance and biofilm compartmentalisation due to differences in metabolisms and sensitivity to toxic stressors. We also show through numerical studies the impact of phage predation on bacterial communities and plasmid spread. This is joint work with Julien Vincent, Alberto Tenore and Luigi Frunzo.

Organized by: Tin Phan (Los Alamos National Laboratory), Yun Kang (Arizona State University); Tracy Stepien (University of Florida)

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

1. Jianhong Wu York University
   "Population dynamics involving perceived risk-structured behavioural changes"
Behaviour changes and intervention takes place in response to perceived risks in the vector-host and pathogen-host interactions, leading to rich and complex population dynamics including multi-stability and oscillation birth and death. We will review a few models and analyses involving coupled systems of delay-differential equations and algebraic-integral equations.
2. Angela Peace Texas Tech University
   "Nutrient-Driven Adaptive Foraging Behaviors"
This study investigates nutrient-driven adaptability of foraging efforts in producer-grazer dynamics of simple food web models. Using dynamical systems theory, we develop and two systems of ordinary differential equations using adaptive dynamics theory; a two-dimensional base model incorporating a fixed energetic cost of feeding and a three-dimensional adaptive model where feeding costs vary over time in response to environmental conditions. By comparing these models, we examine the effects of adaptive foraging strategies on population dynamics. Our adaptive model suggests a potential mechanism for evolutionary rescue, where the population dynamically adjusts to environmental changes—such as fluctuations in food quality—by modifying its feeding strategies. However, when population densities oscillate in predator-prey limit cycles, fast adaptation can lead to very wide amplitude cycles, where populations are endanger of stochastic extinction. Overall, this increases our understanding of the conditions under which nutrient-driven adaptive foraging strategies can yield benefits to grazers.
3. Rebecca Everett Haverford College
   "Stoichiometric ontogenetic development influences population dynamics: Stage-structured model under nutrient co-limitations"
Ecological processes depend on the flow and balance of essential elements such as carbon (C) and phosphorus (P), and changes in these elements can cause adverse effects to ecosystems. The theory of Ecological Stoichiometry offers a conceptual framework to investigate the impact of elemental imbalances on structured populations while simultaneously considering how ecological structures regulate nutrient cycling and ecosystem processes. While there have been significant advances in the development of stoichiometric food web models, these efforts often consider a homogeneous population and neglect stage-structure. The development of stage-structured population models has significantly contributed to understanding energy flow and population dynamics of ecological systems. However, stage structure models fail to consider food quality in addition to food quantity. We develop a stoichiometric stage-structure producer-grazer model that considers co-limitation of nutrients, and parameterize the model for an algae-Daphnia food chain. Our findings emphasize the impact of stoichiometric constraints on structured population dynamics. By incorporating both food quantity and quality into maturation rates, we demonstrate how stage-structured dynamics can influence outcomes in variable environments.
4. Irakli Loladze Bryan College of Health Sciences
   "From Information Strings to Ocean Stoichiometry: Why Life's Atomic Constraints Drive Convergence to the Redfield Ratio"
The Redfield ratio (N:P ≈ 16), a cornerstone of marine biogeochemistry, represents a striking global pattern whose fundamental origins remain debated. Why this specific ratio? This talk presents a perspective rooted in the very nature of biological information. Unlike human technologies that often rely on elementary particles, biological information processing is fundamentally atom-bound. Specifically, genetic information is stored and processed using linear molecular strings – DNA, RNA, and associated proteins. Synthesizing these 'information-rich' molecules imposes non-negotiable demands for specific atoms, particularly nitrogen (N) for proteins and both N and phosphorus (P) for nucleic acids, in precise elemental ratios. These immutable atomic requirements constrain the core cellular machinery of information expression: the coupled synthesis of N-rich proteins and P-rich ribosomal RNA (rRNA). Mathematical modeling reveals that the interplay between translation and transcription creates a powerful biochemical attractor. Under optimal conditions, this balance naturally stabilizes at a protein:rRNA ratio corresponding to an elemental N:P stoichiometry remarkably close to the canonical Redfield value of 16. This biochemically optimal ratio is more than a cellular characteristic; it acts as a dynamic attractor on much larger scales. Incorporating evolutionary dynamics and biogeochemical feedbacks like nutrient recycling (mimicked by an iterative chemostat framework and analyzed using contraction mapping) demonstrates convergence towards N:P ≈ 16. This ratio emerges as an evolutionary stable strategy and a powerful stoichiometric attractor, pulling the system towards Redfield proportions even under varying nutrient limitations over ecological and evolutionary time. This talk proposes that the canonical Redfield ratio is a planetary-scale echo of the fundamental constraints imposed by the need to faithfully replicate and express genetic information using atoms. It shows how the deep rules governing information in biology can sculpt the chemistry of our planet.

Organized by: Abigail Barlow (The University of Bath), n/a

1. Abby Barlow The University of Bath
   "Integrated tick management strategies in fragmented peridomestic environments"
The spirochetal bacterium Borrelia burgdorferi is a tick-borne zoonosis that circulates in various wildlife populations in temperate rural regions of Europe, North America and Asia. Humans are not usually competent for transmission, but spillover infections can lead to Lyme disease (LD). The infection is passed to human hosts via the bite of an infected tick. Ticks have multiple life stages and complex phenology. Over the last decade, there has been a sustained increase in Borrelia prevalence in wildlife in North America, leading to an increase in spillover events, often via residential areas that back onto woodland. Understanding tick ecology is essential for predicting the spread of LD, informing control strategies, and assessing impacts of environmental change. In this talk, we will discuss the development of a tick population model for a fragmented peridomestic environment. We will consider a metapopulation framework of residential patches, where humans might encounter ticks. Our principal goal is to understand the impact of deer dispersal on the tick ecological dynamics. Deer are the primary host for adult ticks and a necessary component of tick reproduction. They visit the residential patches in very small numbers (1 or 2 per hectare/ patch) and can disperse over large distances, transporting any feeding ticks in the process. Consequently, the location of the deer is inherently stochastic and the tick population dynamics are drawn into this stochasticity. Protective measures against LD often involve treating the deer population with an arcarcide-based treatment. We incorporate these features into our model by employing a hybrid modelling framework. Our results will explore the impact that deer dispersal and treatment on the tick population dynamics, in particular on the density of infected nymphs.
2. Folashade B. Agusto University of Kansas
   "Modeling the effect of lethal and non-lethal predation on the dynamics of ticks and tick-borne ehrlichiosis disease"
Tick-borne illnesses, including ehrlichiosis, from both endemic and emerging pathogens have shown a dramatic rise in recent years, posing an increasing public health threat in the United States. However, fewer studies have explored the cascading effects of lethal and non-lethal predation on the dynamics of tick-borne diseases. The fear induced by predators can alter prey behavior, impacting predation rates and ultimately influencing disease transmission dynamics. This study seeks to clarify the effects of both lethal and non-lethal predation through mathematical modeling of tick-borne disease dynamics. Theoretical analysis and sensitivity tests were conducted to examine how fear-driven changes in host behavior affect tick populations and disease prevalence. Stability conditions for various equilibria of the reduced model were established under constant tick fecundity and mortality rates. The study shows that the combined effects of lethal and non-lethal predation trigger a cascade: as predator attack rates rise, prey and tick populations, along with disease prevalence, decrease. Moreover, an increase in predator-induced fear further reduces prey populations, leading to a subsequent decline in tick populations.
3. Kyle Dahlin Virginia Tech
   "Down with the sickness: modelling the effect of disturbed blood-feeding on mosquito-borne disease transmission"
Mosquito-borne pathogens remain a major global health challenge, and transmission depends critically on mosquito blood feeding. This process involves behavioral interactions between mosquitoes and vertebrate hosts, including host defenses that can disturb feeding and increase mosquito mortality. We develop a mathematical model that treats blood feeding as a predator-prey interaction, incorporating mosquito decisions to persist or quit in response to host defense and the associated risk of mortality. The model links individual-level feeding outcomes to population-level traits, such as the average multiple biting number, the gonotrophic cycle duration, and vectorial capacity. We analyze how these traits are shaped by host defensive behavior and mosquito responses, and quantify the resulting effects on disease transmission. The results highlight how host-mosquito interactions can shape key parameters in transmission models and suggest directions for incorporating behavior into epidemiological predictions.
4. Christina Cobbold The University of Glasgow
   "Incorporating adult age dynamics into mosquito population models: implications for predicting abundances in changing climates"
Mosquito-borne diseases (MBDs) pose increasing threats under future climate change scenarios and an understanding of mosquito population dynamics is pivotal to predicting future risk of MBDs. Most models that describe mosquito population dynamics often assume that adult life-history is independent of adult age and yet mosquito senescence is known to affect mosquito mortality, fecundity and other key biological traits. Despite this, little is known about the effects of adult age at the level of the mosquito population, especially under varying temperature scenarios. We developed a stage-structured delayed differential equation model incorporating the effects of the abiotic environment and adult age to shed light on the complex interactions between age, temperature, and mosquito population dynamics. Taking Culex pipiens, a major vector of West Nile Virus, as our study species our results show that failing to consider mosquito senescence can lead to underestimates of future mosquito abundances predicted under climate change scenarios. Moreover at temperature extremes age-dependent mechanisms combined with the effects of density-dependent mortality on the immature stages at also act to decrease mosquito abundances, highlighting a complex interplay between adult aging dynamics and population abundance.

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
   "Social norms and the spread of infectious diseases"
Humans are a hyper-social species, which greatly impacts the spread of infectious diseases. How do social dynamics impact epidemiology and what are the implications for public health policy? We develop a model of disease transmission that incorporates social dynamics and a behavior like a voluntary nonpharmaceutical intervention (NPI) that reduces the spread of disease. We use a 'tipping-point' dynamic, previously used in the sociological literature, where individuals adopt a behavior given a sufficient prevalence of the behavior in the population. The thresholds at which individuals adopt the NPI behavior are modulated by the perceived risk of infection. Social conformity creates a type of 'stickiness' whereby individuals are resistant to changing their behavior due to the population's inertia. In our model, we observe that such behavioural effects can generate very counterintuitive outcomes, such as the outbreak size getting larger as the effectiveness of an intervention increases. These results highlight the complex interplay between the dynamics of epidemics and norm-driven collective behaviors. This is joint work with Bryce Morsky, Felicia Magpantay, and Erol Açkay (See Morsky et al. 2023. PNAS 120(19): 2221479120)
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. Carrie Manore Los Alamos National Labs
   "Designing Models and Forecasts with Non-Traditional Data to Assess Interventions and Prevention"
As the world becomes more connected and ecosystems change, we need adaptive tools to asses how risk is changing and inform options for interventions. We have adapted traditional forecasting and modeling approaches to ingest data that can adapt model parameters and predictions as conditions change. This includes genetic data to capture pathogen evolution and ecosystem or weather data, to fit time varying parameters. Our approach has the potential to increase the accuracy of mathematical or statistical models in predicting changes in dynamics such as the “elbows” in an outbreak or year to year differences in endemic diseases. Examples will include mosquito-borne diseases and seasonal respiratory infections.

Organized by: Sebastian Schreiber (University of California, Davis)

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

1. Alanna Hoyer-Leitzel Mount Holyoke College
   "Resilience to reinfection in an impulsive model of viral exposure"
Re-exposure to virus in an ongoing, low-level endemic can lead to the appearance of long term immunity in an individual. Starting with an ordinary differential equations model for an immune system, we simulate repeated viral re-exposure with a discrete impulse of virus. When the re-exposures are deterministic, we can find different long term outcomes of either reinfection or protection, depending on viral dose size and frequency. We investigate how these outcomes persist when the re-exposures are stochastic. We examine the effects of the choice of probability distributions for viral dose size and frequency.
2. Jakob Kaare-Rasmussen University of California, Davis
   "Habitat Destruction and Disturbance in Forest Ecosystems"
Forests around the world are increasingly threatened by habitat destruction and disturbances—factors that, together, can have profound and often unexpected effects on these ecosystems. Habitat destruction is the loss of habitat due to urbanization or agricultural lands while disturbances are perturbations of the system that leave the environment habitable, like forest fires and drought. Forests are not just collections of trees; they also depend on below-ground mycorrhizal fungal mutualists. The mycorrhizal fungi facilitate the uptake of nutrients and water for the trees while receiving products of photosynthesis in return. Despite their importance and close relationship with trees, mycorrhizal fungi are often overlooked in mathematical models of forest response to environmental stressors. To address this gap, I developed a metacommunity model that explicitly incorporates the mutualism between trees and mycorrhizal fungi. After analyzing the dynamics of the unperturbed system, I examined the impact of habitat destruction—modeled as the continuous loss of habitat over time—which can lead to catastrophic forest collapse. This habitat destruction is often accompanied by disturbance events, modeled here as discrete events that “kick” the system’s state. The interplay between continuous background change (destruction) and sudden disturbances (kicks) generates complex and sometimes counterintuitive behaviors, including rate-induced tipping from a healthy forested state to local extinction. To gain insights into the dynamical mechanisms underlying this rate-tipping, I analyzed a simplified one-dimensional bistable model. This reduced model reveals general patterns relevant to a wide range of systems experiencing both gradual environmental change and discrete disturbance events. Given that many ecological systems are facing similar pressures, such as ongoing environmental degradation combined with frequent disturbances, this work illustrates how non-autonomous flow-kick models can be used to better understand and predict how ecosystems respond to these dual stressors.
3. Vanja Dukic University of Colorado
   "Weak-form inference for hybrid dynamical systems in ecology"
Species subject to predation and environmental threats commonly exhibit variable periods of population boom and bust over long timescales. Understanding and predicting such behaviour, especially given the inherent heterogeneity and stochasticity of exogenous driving factors over short timescales, is an ongoing challenge. A modelling paradigm gaining popularity in the ecological sciences for such multi-scale effects is to couple short-term continuous dynamics to long-term discrete updates. We develop a data-driven method utilizing weak-form equation learning to extract such hybrid governing equations for population dynamics and to estimate the requisite parameters using sparse intermittent measurements of the discrete and continuous variables. The method produces a set of short-term continuous dynamical system equations parametrized by long-term variables, and long-term discrete equations parametrized by short-term variables, allowing direct assessment of interdependencies between the two timescales. We demonstrate the utility of the method for epizootics experienced by the North American spongy moth (Lymantria dispar dispar). Joint work with Dan Messenger and Greg Dwyer.
4. Punit Gandhi Virginia Commonwealth University
   "The impact of rainfall variability on pattern formation in a flow-kick model for dryland vegetation bands"
Water input in dryland ecosystems comes in the form of infrequent, discrete and largely unpredictable rainstorms. These short-lived pulses are known to sustain large-scale spatial patterns that appear as regularly spaced bands of dense vegetation separated by regions of bare soil. I will present a flow-kick modeling framework for such dryland vegetation patterns that treats storms as instantaneous kicks to the soil water, which then interacts with vegetation during the long dry periods between the storms. The spatial profiles of the nonlocal, state-dependent soil water kicks capture positive feedbacks in the storm-level hydrology that act to concentrate water within the vegetation bands. This flow-kick model predicts that variance in rainfall, introduced through randomness in the timing and magnitude of water input from storms, decreases the parameter range over which patterns form and may negatively impact ecosystem resilience. Authors: Matthew Oline (University of Chicago), Mary Silber (University of Chicago)

Organized by: Cody FitzGerald (Northwestern University), Rainey Lyons (CU Boulder), Nora Heitzman-Breen (CU Boulder), Susan Rogowski (NCSU)

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

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

Organized by: James Osborne (University of Melbourne), James Glazier (Indiana University) Yi Jiang (Georgia State University)

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

1. Claire Miller Auckland Bioengineering Institute, NEW ZEALAND
   "Multicellular modelling of endometrial cell invasion in endometriosis lesion onset"
Endometriosis is a chronic gynaecological condition that is estimated to affect 1 in 9 people with a uterus. The disease is characterised by the presence of cells similar to those that line the uterus (endometrial cells) growing as lesions outside the uterus, such as in the lining of the pelvis. It is hypothesised that the disease originates from menstrual debris entering the pelvic region via the fallopian tubes. The endometrial cells in this menstrual debris then breach the epithelial layer lining the pelvis and form lesions that intrude into the lower layers of the tissue. Very little is understood about the conditions required for endometriosis onset. The endometrial cell invasion behaviour has been hypothesised to be a result of dysfunctions in the immune system, the invading endometrial cells, the breached epithelial layer, or any combination of these. In this talk I will present a multicellular agent-based model for endometrial cell invasion of an epithelial monolayer. Using this model, I will explore several of the hypotheses around disease onset, such as those related to cell proliferation and adhesion, and assess the level to which they promote endometrial cell invasion.
2. Paul Macklin Indiana University, USA
   "Intuitive code-free tissue modeling in the cloud with PhysiCell"
Agent-based models (ABMs) simulate individual cells as they move and interact in a virtualized tissue microenvironment (TME). When developing an ABM for a complex multicellular system, a scientist must define diffusible chemical substrates (e.g., oxygen and signaling factors), cell types, and functional relationships between cell behaviors and the chemical and physical signals in the simulated tissue environment. To date, creating an ABM requires scientists to encode these relationships–the “rules” of the cell agents–by hand: first as qualitative statements, then as mathematics, and finally as custom-written simulation code. As a result, ABMs take substantial time to develop and debug, and their code is neither interpretable nor reusable. In this talk, we describe a new (recently published), intuitive cell behavior grammar that writes ABM rules with human-interpretable language (e.g., “IL6 increases migration speed”), and directly and uniquely transforms these interpretable statements into mathematics and model code at run-time without need for hand coding. We also show a graphical studio (PhysiCell Studio) that allows scientist users to rapidly create, explore, and refine these code-free models on the desktop or in the cloud. We show examples from cancer hypoxia, immunology, neurodevelopment, and combination cancer treatments. Beyond the reference implementation in the PhysiCell ABM framework, the modeling grammar could provide a basis for model annotation and exchange between open source simulation toolkits, including “virtual cell templates” (digital cell lines) that bundle a cell type with base behavioral parameter values and cell rules written in this grammar.
3. Steve Runser ETH Zurich, SWITZERLAND
   "PolyHoop & SimuCell3D: Efficient and Versatile Tissue Simulations in 2D and 3D"
Accurate simulation of epithelial tissue dynamics requires models that capture complex, polarized cell shapes with high spatial resolution. Previous approaches were hampered by high computational cost or lacked essential biological detail. To overcome these challenges, we developed two powerful new computational frameworks for simulating epithelial tissues in 2D and 3D. PolyHoop [Vetter, Runser & Iber, Comput. Phys. Commun. 299, 109128 (2024)] models cell membranes as closed flexible hoops in 2D, incorporating intra- and intercellular forces and topological events such as cell division and fusion. SimuCell3D [Runser, Vetter & Iber, Nat. Comput. Sci.] extends this approach to 3D, using triangulated surfaces to represent membranes, nuclei, and extracellular matrices, with an algorithm that automatically polarizes cells. Both tools are highly efficient, enabling simulations of hundreds of thousands of deformable epithelial cells with unprecedented spatial fidelity. In this talk, I will demonstrate how these models reproduce key epithelial features and support applications including cancer growth, cell migration, and tissue stratification dynamics.

Organized by: Laurent PUJO-MENJOUET and Suzanne SINDI (Claude Bernard Lyon 1 University (Lyon, FRANCE))

1. Théo LOUREAUX University of California, Merced
   "Modeling the Prion Aggregation Process During Polymerization Experiments Using Delay Differential Equations"
Prion proteins are notorious for their ability to induce neurodegenerative diseases by forming long fibrillar aggregates that accumulate in the brain. While the aggregation of these proteins and their fragmentation by oligomeric species is central to disease progression, the underlying mechanisms remain poorly understood. To better interpret experimental data, mathematical models have been developed to translate the key chemical reactions governing this process. In this talk, I present a novel modeling approach based on delay differential equations (DDEs), designed to capture the time-dependent features of prion polymerization dynamics. I will demonstrate how this framework aligns with experimental observations from polymerization assays in which prion monomers are thermally induced to aggregate. The model not only fits the data well but also suggests an alternative perspective on the interplay between aggregation and fragmentation, offering a new theoretical lens on prion dynamics.
2. Ashish Raj University of California San Francisco
   "Biophysical modeling of pathology progression in dementia and its implementation using physics-informed neural networks"
This presentation will focus on developing mathematical and computational models that use the brain’s structural connectivity to predict the development of brain diseases, including Alzheimer’s, Parkinson’s, Huntington’s, ALS and other neurodegenerative diseases. I will first describe our original proposal that Alzheimer and other dementias are underpinned by misfolded pathologies that spread on the brain structural connectome. This process can be mathematically captured by the so-called 'Network Diffusion Model'. Several examples from AD, ALS, Huntington's, Parkinson's and other dementias will be demonstrated. I will then present new extensions of this model in many meaningful ways, incorporating protein aggregation, clearance, active axonal transport, and mediation by external genes, cells and neuroinflammation. Deep neural network implementations of these complex and computationally prohibitive models will be motivated, and preliminary work on physics-informed neural networks will be presented. I will also briefly describe recent work in modeling brain electrophysiology using similar graph spectral models. All above models centrally involve the brain’s complex network Laplacian eigen-spectrum and “graph harmonics.” Through this work, we have found significant differences in the model’s parameters that relate healthy brains to Alzheimer’s disease, sleep, epilepsy and infant brain maturation. The related papers will be briefly highlighted.
3. Human Rezaei INRAE, Jouy-en-Josas FRANCE
   "Intrinsic Dynamics and Deterministic Diversification Drive a New Model of Prion Replication and Dissemination"
Through experimental approaches combining nanoscale infrared spectroscopy and dynamic atomic force microscopy, we investigated the intrinsic dynamics of PrPSc assemblies outside the context of templated replication. These studies revealed that PrPSc assemblies exhibit an inherent capacity for structural diversification and material exchange, leading us to establish a new replication model. This model incorporates deterministic structural diversification and proposes that prion assemblies can undergo catalytic conformational transitions independently of replication events, challenging the notion that replication alone governs strain specificity. Building on these findings, we developed a stochastic reaction-diffusion framework that integrates nonlinear replication dynamics and tissue responses. Using the Gillespie algorithm, we modeled neuroinvasion as a complex and emergent process shaped by strain-specific PrPSc behavior and anatomical connectivity. This integrative approach offers new insights into how structural diversity is maintained within populations of prions and how it contributes to strain-dependent tropism and pathogenesis. By shifting the focus from purely replication-driven models to those considering intrinsic structural dynamics, this work proposes a revised conceptual framework for prion propagation, with broader implications for other protein misfolding diseases.
4. Laurent Pujo-Menjouet University Claude Bernard Lyon 1 - Camille Jordan Institute
   "Modeling the formation of perinuclear crowns made of agglutinated ATM proteins observed in fibroblasts from patients affected by Alzheimer’s disease"
Alzheimer’s disease is a progressive neurodegenerative disorder marked by the irreversible loss of brain cells. In response to oxidative stress, ATM proteins typically migrate to the nucleus to detect and repair double-strand DNA breaks. However, recent studies suggest that APOE proteins may accumulate at the nuclear envelope, blocking the entry of ATM proteins and resulting in the formation of a characteristic perinuclear crown. To better understand this phenomenon and evaluate potential therapeutic interventions, we propose two modeling approaches: a compartmental model and a reaction-diffusion system that capture the physical interactions between ATM and APOE proteins. Both models incorporate key biological processes, including protein transport, monomer aggregation, and the dissociation of dimers and complexes. We explore the effects of irradiation and antioxidant treatments on the disintegration of the perinuclear crown. Our simulations suggest that the combined use of these two strategies is the most effective in delaying crown reformation, highlighting a promising therapeutic avenue for Alzheimer’s disease.

Organized by: Yangjin Kim (Brown University and Konkuk University), Magdalena Stolarska at University of St. Thomas

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

1. Magda Stolarska University of St. Thomas
   "A mathematical model of active cortical stress generation and its effect on cell movement"
When moving through a confined, fibrous extracellular environment, many cells use an amoeboid mode of cellular motility. In particular, it is well known that cancer cells can undergo a mesenchymal-amoeboid transition under certain conditions. Amoeboid motility is characterized by weak adhesions to the extracellular environment, a rounded morphology, and flow of the actin cortex. A related, yet simpler, mode of cell motility is cellular swimming. In eukaryotic cell swimming, it is known that active deformation of the cortex induces attachment-free movement through a fluid, but much of the details of this process are not well understood. In this talk, I will present a mathematical model that aims to begin investigating how variability in actomyosin activity in the cortex, properties of the cortex-membrane (ERM) attachment proteins, and the mechanical properties of the microenvironment affect cell movement through a fluid. The hybrid model presented models the intra- and extra-cellular fluid as a continuum and treats the membrane and cortex and a discrete system of connected segments and nodes. By using the finite element method to solve the model equations, we are able to analyze how varying various properties of this system affects cellular swimming velocities.
2. Dumitru Trucu University of Dundee
   "Advancements in multiscale modelling for glioblastoma: emergence of 'on-the-fly' non-local isotropic-to-anisotropic transition in cell population transport"
Despite all recent in vivo, in vitro, and in silico advances, the understanding of the genuine biologically multiscale process of solid tumour invasion remains one of the greatest open questions for scientific community. In this talk we present recent mathematical multiscale moving boundary modelling advancements for solid tumour invasion, with special focus on glioblastoma progression. We focus on enhancing the mathematical modelling for key aspects of the dynamic interactions that the migratory cancer cells population and the accompanying matrix degrading enzymes (MDEs) have with the extracellular matrix (ECM) components, and, in particular, with the ECM fibres. These are complex interactions enabled by a complicated series of integrated multiscale systems, which are at least two-scale in nature and share (and contribute to) the same tumour macro-dynamics (i.e., tissue-scale dynamics) but have independent-in-nature micro-dynamics (i.e., cell-scale dynamics), and despite previous modelling progress, these deserve significant renewed research efforts. Specifically, this talk we seek to address: (1) the enhancing effect of the interfacial presence of ECM fibres on the macro-scale tumour boundary movement; (2) a new non–local “go-or-grow” perspective on the motility of cancer cel population; and (3) the emerging “on-the-fly” non–local isotropic – to – anisotropic transition in the diffusive cell population transport. Mathematical formulations for all these aspects are proposed analytically and then explored computationally and discussed in the context of glioblastoma progression.
3. Padmini Rangamani University of California San Diego
   "Modeling collagen fibril degradation as a function of matrix microarchitecture"
Collagenolytic degradation is a process fundamental to tissue remodeling. The microarchitecture of collagen fibril networks changes during development, aging, and disease. Such changes to microarchitecture are often accompanied by changes in matrix degradability. In a matrix, the pore size and fibril characteristics such as length, diameter, number, orientation, and curvature are the major variables that define the microarchitecture. In vitro, collagen matrices of the same concentration but different microarchitectures also vary in degradation rate. How do different microarchitectures affect matrix degradation? To answer this question, we developed a computational model of collagen degradation. We first developed a lattice model that describes collagen degradation at the scale of a single fibril. We then extended this model to investigate the role of microarchitecture using Brownian dynamics simulation of enzymes in a multi-fibril three dimensional matrix to predict its degradability. Our simulations predict that the distribution of enzymes around the fibrils is non-uniform and depends on the microarchitecture of the matrix. This non-uniformity in enzyme distribution can lead to different extents of degradability for matrices of different microarchitectures. Our simulations predict that for the same enzyme concentration and collagen concentration, a matrix with thicker fibrils degrades more than that with thinner fibrils. Our model predictions were tested using in vitro experiments with synthetic collagen gels of different microarchitectures. Experiments showed that indeed degradation of collagen depends on the matrix architecture and fibril thickness. In summary, our study shows that the microarchitecture of the collagen matrix is an important determinant of its degradability.
4. Noe Mercado Warren Alpert Medical School, Brown University
   "Impact of Cytomegalovirus on Glioblastoma progression"
Background: Glioblastoma (GBM) is the most common primary malignant brain tumor and has no effective treatments. Human Cytomegalovirus (HCMV) has been implicated in GBM progression and antiviral drugs like Cidofovir (CDV) have promising activity in GBM. Previously we reported that in our established syngeneic GBM mouse model perinatally infected with murine cytomegalovirus significant reduction in overall survival compared to uninfected controls. Treatment with CDV improved survival in infected mice and inhibited MCMV reactivation as well as tumor angiogenesis. However, the molecular mechanisms of antiviral drug treatment on GBM have not been studied. Results: Here we show that GBM patient-derived glioma stem cells (GSCs) are highly permissive to HCMV infection compared to established GBM lines commonly used in in vitro (U-373). Neuronal cells that are found in the tumor microenvironment also have high permissiveness to infection although viability significantly decreased post infection. Treatment with antiviral drug Brincidofovir (BCV), a lipid prodrug of cidofovir, significantly reduced viral infection but did not directly induce GBM cell killing. When cells were treated with standard of care (SOC) therapy comprising irradiation (6Gy) and temozolomide (TMZ), resistance to cell death was observed in infected GSCs. This phenotype was reversed by treatment with BCV in a dose-dependent manner. These observations suggest that HCMV induces resistance to SOC in GSCs which may promote GBM progression, and this may be a target of antiviral therapy. Proteomic analysis of infected GSCs revealed upregulation of several pro-tumorigenic proteins including Structural Maintenance of Chromosome 4 (SMC4), WD repeat domain 5 (WDR5) and thymocyte selection associated high mobility group (TOX). Interestingly upon antiviral drug treatment these proteins were no longer upregulated and instead several were significantly downregulated after BCV treatment. Conclusions: Together these data suggest that HCMV may promote tumorigenesis in part due to the glioma stem cell niche. After infection these glioma stem cells are more resistant to chemoradiotherapy which can be overcome by antiviral drug (BCV) treatment. These data provide mechanistic evidence for the role of HCMV in GBM and support ongoing research into antiviral drug approaches in the clinic.

Organized by: Fanze Kong (University of Washington), Michael Jeffrey Ward and University of British Columbia

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

1. Jack Hughes University of British Columbia
   " Pulses, Waves, and Mesas in Mass Conserved Reaction-Diffusion Media: From Theory to Actin Polymerization"
The transition from random walk to directional propagation (and back) is one of the intriguing phenomena observed in motile eukaryotic cells. However, typically, theoretical studies distinguish between the two phenomena and focus either on dissipative models or models obeying gradient flows, respectively. Using a three-variable dissipative reaction-diffusion system with mass conservation modelling patterns in the cortex of cells, we show how pulses, waves, fronts, and (stationary) mesas generically organize about high codimension bifurcations. Specifically, we demonstrate the novelty of mass conservation, which enters via a long-wavenumber bifurcation of a large-scale mode. Lastly, following the biological interest, we will address the bistability between travelling wave and wave-pinning solution branches, which emerge from a codimension-2 bifurcation to a finite wavenumber Hopf and a conserved large-scale mode.
2. Thomas Hillen University of Alberta
   "Mean First Passage Times for Transport Equations"
Many transport processes in ecology, physics and biochemistry can be described by the average time to first find a site or exit a region, starting from an initial position. Here, we develop a general theory for the mean first passage time (MFPT) for velocity jump processes. We focus on two scenarios that are relevant to biological modelling; the diffusive case and the anisotropic case. For the anisotropic case we also perform a parabolic scaling, leading to a well known anisotropic MFPT equation. To illustrate the results we consider a two-dimensional circular domain under radial symmetry, where the MFPT equations can be solved explicitly. Furthermore, we consider the MFPT of a random walker in an ecological habitat that is perturbed by linear features, such as wolf movement in a forest habitat that is crossed by seismic lines. (Joint work with M. D'Orsogna, JC. Mantooth, AE. Lindsay)
3. Chunyi Gai The University of Northern British Columbia
   "An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains"
Pattern formation on growing domains is one of the key issues in developmental biology, where domain growth has been shown to generate robust patterns under Turing instability. In this work, we investigate the mechanisms responsible for generating new spikes on a growing domain within the semi-strong interaction regime, focusing on three classical reaction-diffusion models: the Schnakenberg, Brusselator, and Gierer-Meinhardt (GM) systems. Our analysis identifies two distinct mechanisms of spike generation as the domain length increases. The first mechanism is spike self-replication, in which individual spikes split into two, effectively doubling the number of spikes. The second mechanism is spike nucleation, where new spikes emerge from a quiescent background via a saddle-node bifurcation of spike equilibria. Critical stability thresholds for these processes are derived, and global bifurcation diagrams are computed using the bifurcation software pde2path. These results yield a phase diagram in parameter space, outlining the distinct dynamical behaviors that can occur.
4. Alan Lindsay University of Notre Dame
   "Asymptotic and numerical methods for cellular signaling and directional sensing"
Diffusive arrivals to membrane surfaces provide cues for cellular decision making, for example when and where to move. In this talk we will describe the advancement of both asymptotic and numerical methodologies to describe and interpret these signals. A particular focus of these new methods are to describe the full time dependent fluxes over the cell surface during signaling processes. We will show several examples how early arrivals to the cell surface, combined with cellular geometry, can increase the strength and quality of directional signaling.

Organized by: Sungrim Seirin-Lee (Kyoto University/Graduate School of Medicine), Jaekyoung Kim (KAIST), So Miyoshi (Pfizer)

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

1. Sungrim Seirin-Lee Kyoto University
   "Pathological State Inference System based on Skin Eruption Morphology for Personalized Treatments in Dermatology"
Skin diseases typically appear as visible information-skin eruptions distributed across the body. However, the biological mechanisms underlying these manifestations are often inferred from fragmented, time-point-specific data such as skin biopsies. The challenge is further compounded for human-specific conditions like urticaria, where animal models are ineffective, leaving researchers to rely heavily on in vitro experiments and sparse clinical observations. In this presentation, I propose a novel mathematical modeling framework that bridges the gap between the visible geometry of skin eruptions and the invisible molecular and cellular dynamics driving them. This interdisciplinary approach integrates mathematical science, data-driven analysis, and clinical dermatology to overcome current limitations in understanding disease pathophysiology. Furthermore, I will introduce an innovative methodology that combines mathematical modeling with topological data analysis, allowing for the estimation of patient-specific parameters directly from morphological patterns of skin eruptions. This framework offers a new pathway for personalized analysis and mechanistic insight into complex skin disorders.
2. Alexander Anderson Moffitt Cancer Center
   "Adaptive Therapy from Board to Bench to Bedside and Back Again"
Our current approach to cancer treatment has been largely driven by finding molecular targets, those patients fortunate enough to have a targetable mutation will receive a fixed treatment schedule designed to deliver the maximum tolerated dose (MTD). Cancers are complex evolving systems that adapt to therapeutic intervention through a suite of resistance mechanisms, therefore whilst MTD therapies generally achieve impressive short-term responses, they unfortunately give way to treatment resistance and tumor relapse. The importance of evolution during both tumor progression, metastasis and treatment response is becoming more widely accepted. However, MTD treatment strategies continue to dominate the precision oncology landscape. Evolutionary therapy is a new evolution inspired treatment paradigm that seeks to exploit how a cancer evolves under treatment through smart drug dosing and sequencing often informed by mathematical modelling. Adaptive therapy is an evolutionary therapy that aims to slow down the emergence of drug resistance by controlling tumor burden through competition between drug sensitive and resistant cell populations. Adaptive therapy specifically alters the treatment schedule (timing and dose) in response to a patient’s disease dynamics, often stopping therapy or deescalating dose when burden is low and starting therapy or increasing dose when burden is high. This approach was inspired by pest management and developed through mathematical model driven insights and has been shown to work in preclinical animal models (prostate, ovarian, melanoma, breast) and in pilot clinical trials (NCT02415621; NCT05189457; NCT03543969). Recently, phase 2 adaptive therapy trials in prostate (NCT05393791) and ovarian cancer (NCT05080556) are testing the treatment break and treatment deescalation approaches respectively. In this talk we will discuss different aspects of adaptive therapy including (i) How to pick patients who will benefit from it; (ii) How best to optimize the treatment switch threshold; (iii) The importance of appointment frequency; (iv) Robustness when patients miss appointments. We will utilize differential equation and cellular automata models as well as deep reinforcement learning.
3. Adrien Hallou University of Oxford
   "Spatial mechano-transcriptomics: mapping at single-cell resolution mechanical forces and gene expression in tissues"
Advances in spatial profiling technologies are providing insights into how molecular programs are influenced by local signalling and environmental cues. However, cell fate specification and tissue patterning involve the interplay of biochemical and mechanical feedback. Here, we propose a new computational framework that enables the joint statistical analysis of transcriptional and mechanical signals in the context of spatial transcriptomics. To illustrate the application and utility of the approach, we use spatial transcriptomics data from the developing mouse embryo to infer the forces acting on individual cells, and use these results to identify mechanical, morphometric, and gene expression signatures that are predictive of tissue compartment boundaries. In addition, we use geoadditive structural equation modelling to identify gene modules that predict the mechanical behaviour of cells in an unbiased manner. This computational framework is easily generalized to other spatial profiling contexts, providing a generic scheme for exploring the interplay of biomolecular and mechanical cues in tissues.
4. Jae Kyoung Kim KAIST
   "Improving Biological Predictions: Rethinking Markovian and Diffusion Assumptions"
Mathematical modeling plays a critical role in understanding complex biological systems and making accurate predictions. However, incorrect probabilistic assumptions embedded in mathematical models can lead to significant errors. In this talk, I will highlight two such cases. First, I will discuss how the unrealistic assumption of Markovian dynamics in modeling the latent period of infectious diseases can produce misleading predictions about the spread of COVID-19, and present methods to overcome this issue. Second, I will address the limitations of the widely-used Fick’s law in describing molecular diffusion within cells. Contrary to experimental observations, Fick’s law cannot accurately reproduce the tracked movement of molecules. Instead, Chapman’s law, which accounts for physical interactions with cellular structures such as the endoplasmic reticulum, provides a more accurate depiction of intracellular protein diffusion.

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-2.

1. Scott McKinley Tulane University
   "Robust inference and model selection for particle tracking in live cells"
There is now an expansive collection of mathematical work on building models for the transport of intracellular cargo by molecular motors. Commonly studied cargo undergo “saltatory” motion (bidirectional ballistic motion, intermixed with periods of stationarity) along often unobserved microtubules. Traditionally microparticle transport is quantified in terms of mean-squared displacement, but this ubiquitous statistic averages over periods of motion and pauses, eliminating important biophysical information. In this talk, I will discuss our group’s approach to segmentation analysis: an in-house changepoint detection algorithm coupled with a focus on summary statistics that are robust with respect to the inevitable mistakes that changepoint detection algorithms make.
2. Peter Kramer Rensselaer Polytechnic Institute
   "Molecular Mechanisms in Actively Driven Passively Crosslinked Microtubule Pairs"
We apply stochastic modeling to interpret in vitro experiments involving microtubules interacting with the passive crosslinker PRC1 while being crowdsurfed by kinesin in a gliding assay configuration. When an antiparallel pair of microtubules is crosslinked by PRC1, the kinesin slides the microtubules apart while the PRC1 resists this separation. We examine molecular-scale mechanisms for the two distinct modes of resistance which are observed in experiments. We further describe a supporting model for how the microtubules being slid by kinesin respond to the load from the PRC1 crosslinkers.
3. Yangyang Wang Brandeis University
   "A conceptual framework for modeling a latching mechanism for cell cycle regulation"
Two identical van der Pol oscillators with mutual inhibition are considered as a conceptual framework for modeling a latching mechanism for cell cycle regulation. In particular, the oscillators are biased to a latched state in which there is a globally attracting steady-state equilibrium without coupling. The inhibitory coupling induces stable alternating large-amplitude oscillations that model the normal cell cycle. A homoclinic bifurcation within the model is found to be responsible for the transition from normal cell cycling to endocycles in which only one of the two oscillators undergoes large-amplitude oscillations.
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.