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-3.

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

Organized by: Laura Wadkin (Newcastle University), Patrick Parkinson (Newcastle University)

1. Laura Wadkin Newcastle University
   "Optimising stem cell therapies for corneal damage: insights from clinical trial image analysis"
Limbal stem cell deficiency (LSCD) is an ocular disease characterized by a loss or deficiency of the stem cells in the limbus, which are vital for ensuring homeostasis of the corneal epithelium. When these stem cells are lost, the corneal epithelium breaks down becoming scarred and chronically inflamed, resulting in vision loss, chronic pain and photophobia. Treatment of LSCD takes the form of an ex-vivo cultured limbal stem cell (LSC) transplant into the affected eye. Although proven effective at restoring vision, much remains to be understood about the mechanics of corneal epithelium recovery following the LSC transplant. Our research aims to utilise the power of statistical image analysis and mathematical modelling to answer fundamental questions about the condition of the corneal epithelium in an LSCD affected eye, the proliferation and behaviours of LSCs following transplant, and how these behaviours result in the complete restoration of the corneal epithelium. Here, we analyse IVCM images from patients with total unilateral LSCD, taken before and after LSC transplant, to explore potential quantitative diagnostic and monitoring measures of the corneal recovery process.
2. Joel Vanin Biocomplexity Institute/Indiana University Bloomington
   "V-Cornea: A Multiscale Virtual Tissue Approach to Modeling Corneal Biology"
V-Cornea addresses key limitations in ocular irritation assessment methods through a computational framework for predicting corneal epithelial response to injury. Implemented in CompuCell3D, this agent-based model successfully simulates corneal epithelial homeostasis and recovery patterns following trauma or toxicant exposure. The model incorporates biologically-inspired rules governing cell behaviors (proliferation, differentiation, death) and critical signaling pathways including Epidermal Growth Factor (EGF). Our simulations accurately reproduce normal corneal architecture and predict healing timeframes of 3-5 days for slight and mild injuries, consistent with experimental observations. For moderate injuries involving basement membrane disruption, the model demonstrates extended recovery times and emergent structural disorganization that mimics recurrent corneal erosions. Our current work explores supplementary approaches to understand cellular responses to IL-1 signaling, particularly how contextual factors in the extracellular matrix influence diverse outcomes like death, proliferation, and differentiation. We're also investigating how barrier function loss in superficial cells relates to early corneal opacity through a dedicated hydration model. To make these computational tools accessible to non-programmers, we've developed a user-friendly graphical interface (GUI) that facilitates model parameter adjustment, simulation execution, and results visualization. This virtual-tissue approach, now more accessible through the GUI, shows promise for toxicological assessments and therapy optimization by providing a platform to test interventions across various injury scenarios.
3. Patricia Lamirande University of Oxford
   "Mathematical modelling of ocular drug delivery using mean first passage time"
Wet age-related macular degeneration is a progressive disease that can lead to severe visual impairment. Standard treatment involves repeated intraocular drug injections, typically administered monthly, highlighting the need to understand factors influencing drug retention and clearance. Mathematical modelling provides a powerful approach to studying these processes and can offer insights into the development of longer-lasting treatments. In this work, we present a mean first passage time (MFPT) modelling framework to investigate ocular pharmacokinetics and scaling relationships, examining the effects of injection location and anatomical variability. The MFPT quantifies the average time for a randomly diffusing particle to reach a target, making it well-suited for assessing drug distribution and clearance. We formulate a partial differential equation system describing the MFPT of a particle diffusing in a 3D finite domain, modelling the diffusion of ocular pharmaceutics in the eye. Our model quantifies how physiological and anatomical parameters influence the protein therapeutics kinetics (like vitreous half-life), compares interspecies and intraspecies variability, and evaluates the impact of injection site. We validate the modelling framework by comparing its predictions to detailed 3D anatomical scans of rabbit eyes and in vivo pharmacokinetics data from the same eyes, assessing its ability to capture key features of ocular drug transport.

Organized by: Keisha Cook, Anna Nelson (Clemson University), Alessandra Bonfanti (Politecnico di Milano) Giulia Celora (University of Oxford) Kelsey Gasior (University of Notre Dame) Qixuan Wang (University of California, Riverside)

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

1. Khanh Dao Duc University of British Columbia
   "Optimal Transport based metrics and statistics for quantifying cell shape heterogeneity"
Recent advances in experimental methodologies and community efforts have led to a surge in large cell image datasets, that require the developments of new methods to analyze them and extract meaningful information. In this context, I will describe our recent efforts to leverage optimal transport theory, with the introduction of metrics inspired by Wasserstein/Gromov-Wasserstein distances for 2D and 3D cell shapes, that are efficient to compute and can be used for a variety of tasks, including Dimensionality reduction, statistical testing and machine learning. Real data applications will focus on analyzing 2D contour of cancer cells, and 3D images of nucleus and cell shapes under different stages of development.
2. Peijie Zhou Peking University
   "Towards AI Virtual Cell Through Dynamical Generative Modeling of Single-cell Omics Data"
Reconstructing continuous cellular dynamics from sparse, high-dimensional single-cell omics data remains a fundamental challenge in systems biology. Recently, a paradigm shift has been witnessed by leveraging artificial intelligence—specifically, dynamical generative modeling—to develop an AI virtual cell, a predictive digital twin capable of simulating cellular behavior across time and space. In this talk, we introduce our recent attempts that integrate flow-based generative models with partial differential equations (PDEs) to infer latent dynamics from scRNA-seq data. For spatial transcriptomics data, we extend this method with stVCR, a generative model that aligns transcriptomic snapshots across biological replicates and temporal stages. To further infer stochastic dynamics from static data, we explore a regularized unbalanced optimal transport (RUOT) formulation and its theoretical connections to the Schrödinger Bridge and diffusion models. I will also introduce a generative deep-learning solver designed for this problem.Together, these works suggest how generative AI could have the potential to unify dynamical modeling, spatial reconstruction, and stochastic inference—transforming fragmented omics data into a predictive virtual cell.
3. Amanda Alexander University of Houston
   "Persistence of plasmid DNA in spatially organized bacterial populations"
Bacterial cells contain extrachromosomal DNA molecules called plasmids. In nature, plasmids often confer antibiotic resistance. Cells commonly have no mechanism for evenly partitioning plasmids during cell division, and thus there is some probability that one of two daughter cells does not inherit any plasmids. On the population scale, what factors influence the persistence of plasmid DNA over generations? Mathematical modeling is useful in answering this question, as it is difficult to experimentally resolve new plasmid loss from replication of previously plasmid-free cells over long time periods. We introduce a spatial Moran-like model of a finite cell population undergoing plasmid loss, because biologists frequently observe cell populations in spatially constrained microfluidic traps. We explore how properties of single cells impact the dynamics of the cell population in different trap geometries. This analysis reveals that the persistence of plasmid DNA in cell populations has a complex dependence on both spatial geometry and assumptions on single cell properties such as cell division age.
4. Grace McLaughlin University of North Carolina, Chapel Hill
   "Modeling Asynchronous Nuclear Division in Fungal Cells"
Multinucleate cells are common in biology, with examples including muscle cells, placenta, and fungi. Despite this, many aspects of their cell biology are not well understood. Nuclei within these large cells can undergo division, and their cell cycles are governed by biochemical oscillators. Dividing nuclei residing in a common cytosol would be expected to synchronize, as the oscillating levels of cell cycle regulators from each nucleus should in theory entrain neighbors. However, in the multinucleate fungus Ashbya gossypii, spatially neighboring nuclei have been observed to divide out of sync. Despite this apparent nuclear autonomy, nuclear density is controlled within a whole cell, suggesting cell cycles are coupled with cell growth. Does nuclear asynchrony play a role in regulating nuclear density? How do nuclei maintain asynchrony while coordinating their cell cycles on the whole-cell level? And how do nuclei achieve local asynchrony while sharing a common cytosol and originating from the same initial nucleus? To answer these questions, we model Ashbya nuclei as a dynamically growing system of coupled phase oscillators residing within a network-like cell. We find that robust control of nuclear density requires regulation of both cell morphology and cell cycle length. Furthermore, we show that even if cell cycles are coupled to changing nuclear density, it is still possible for them to stay asynchronous as long as this coupling is sufficiently weak. Finally, focusing on interactions between individual nuclei, we find that asymmetric coupling from mitotic nuclei towards younger nuclei can promote asynchrony. All together, these results show how asynchrony can persist in Ashbya, and how these cells achieve a balance between local autonomy with global coordination.

Organized by: Terry Easlick (Univeristé de Montréal/Centre de recherche Azrieli du CHU Sainte-Justine), Morgan Craig, Univeristé de Montréal/Centre de recherche Azrieli du CHU Sainte-Justine

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

1. Jane Heffernan York University
   "The Malaria Parasite Life-Cycle"
We have developed a model of the malaria parasite life-cycle in the blood stage. A system of partial differential equations is employed and models maturation and differentiation of five phases within this stage. The model is used to study possible therapeutic vaccine targets for effective parasite control and eradication.
2. Solène Hegarty-Cremer Université de Montréal
   "Analysing Immune Dysregulation in Vitamin A Deficient Mice During Influenza A Infection"
Influenza virus results in varied infection outcomes and causes significant mortality and morbidity worldwide. Vitamin A deficiency (VAD) is common in both developed and developing countries and has recently been discovered as a comorbidity of influenza A. During influenza infection, VAD mice exhibit dysregulated immune function, with increased viral titers, delayed viral clearance, and elevated levels of inflammatory cytokines. Understanding the interactions between the immune response and vitamin A is critical in addressing this comorbidity. Mathematical models are effective tools to understand and disentangle the complex dynamics of within-host immune responses to respiratory infections. Models for the response to influenza have identified nonlinear relationships between infected cell clearance by CD8+ T cells and infected cell density as well as factors influencing time to recovery. From viral titers, CD8+ T cell counts, and weight loss data in VAD and control murine models during influenza infection, we calibrated a within-host mechanistic mathematical that considers the nonlinear relationships between viral load, infected cells, and effector and memory CD8+ T cells. Through parameter estimation and sensitivity analyses, we found that differences in viral dynamics arise through reduced T cell recruitment and proliferation in VAD mice, as well as an impaired innate immune response. This new mechanistic understanding of the links between retinol and the immune response to influenza will allow for a clearer understanding of VAD and its comorbidity mechanisms and thus enhance our ability to forecast disease progression and combat acute illness from influenza, with potential impacts on other viral infections.
3. Stanca M. Ciupe Virginia Tech
   "Immune system onset and reaction against viral diseases"
Uncertainty in parameter estimates from fitting mathematical models to empirical data limits the model’s ability to uncover mechanisms of interaction. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, I will present several methodologies that can help determine when a model can reveal its parameters. I will apply them in the context of virus infections in animals and humans at within-host, population, and multiscale levels.  Using these approaches, I will provide insight into the sources of uncertainty and provide guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions. 
4. Terry Easlick Université de Montréal
   "Stochastic Methods for modelling antigen-specific cell-mediated immune response"
Cell-mediated immune responses to antigenic stimulation involve a range of stochastic processes, from individual cell fate decisions to population-level dynamics. These responses are shaped by randomness at multiple biological scales, motivating the use of probabilistic models to capture variability and rare events. We will consider how stochastic methods can be used in modelling antigen-specific immunity. The focus is on understanding how noise and structure interact in shaping immune outcomes.

Organized by: Dr Macauely Locke (Los Alamos National Laboratory), Dr Jasmine Kreig, Dr Aurelien Marc, Los Alamos National Laboratory

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

1. Aurelien Marc Los Alamos National Laboratory
   "Modelling shows novel polymerase inhibitor AT-511 (Bemnifosbuvir) demonstrates dual activity against both production and assembly/secretion of hepatitis C virus."
Bemnifosbuvir (BEM) is a novel polymerase inhibitor currently under investigation for the treatment of hepatitis C virus (HCV) infection. In this study, we developed a joint pharmacokinetic and viral dynamic model to characterize the antiviral effects of BEM. Using data from a phase 2 clinical trial and in vitro studies comparing multiple drug candidates, we identified a dual mode of action for BEM—significantly reducing both viral production and virion assembly/secretion, with estimated efficacies of 96% and 98%, respectively. These effects were consistent across multiple HCV genotypes and in patients with cirrhosis. Our findings highlight BEM’s potential as a highly effective, multi-targeting antiviral agent for HCV therapy.
2. Nathanael Hoze IAME
   "Integrating multiscale mathematical modeling and serology to unravel antibody dynamics and infection risk"
: Understanding infectious disease dynamics requires connecting processes across biological scales, from individual immune responses to population-level transmission. Serological data—particularly age-stratified antibody measurements—are a rich resource for inferring historical pathogen circulation and quantifying infection risk, especially in settings lacking continuous surveillance. In this talk, I will present a suite of Bayesian statistical models that leverage serological data to infer key epidemiological and immunological parameters. I begin with models analyzing cross-sectional seroprevalence data, where age profiles inform the reconstruction of time-varying force of infection. These serocatalytic models account for features such as lifelong or waning immunity, heterogeneous exposure, and imperfect diagnostics. Inference is performed via Hamiltonian Monte Carlo using Stan, and the framework is implemented in a dedicated R package, Rsero, which includes tools for model fitting, diagnostics, and model selection using LOOIC and DIC. Analysis of serological data is often dogged by complex immune mechanisms that makes their interpretation difficult. Antibody cross-reactivity, especially relevant in arbovirus serology, happens when viruses can generate antibodies with similar responses. Determining which virus generated the response is challenging. I developed hierarchical Bayesian models that integrate individual-level quantitative titer data with transmission dynamics and prior knowledge on cross-reactive immune responses. These models estimate individual infection histories, pathogen-specific forces of infection, and cross-reactivity structures, using latent variable methods implemented in rstan. The framework accommodates diverse data types, including spatial and demographic covariates. I will also present ongoing work on Enterovirus EV-A71, the main causative agent of hand-foot-and-mouth disease, based on a yearly repeated dataset of age-stratified neutralizing antibody titers collected over 18 years in Malaysia. This model extends classical serocatalytic approaches by modeling full titer distributions across age and time, incorporating mechanisms for infection-induced boosting, waning, and identifying protection due to antibody and number of infections.
3. Quiyana Murphy Virginia tech
   "Understanding antibody durability and magnitude following vaccination against SARS-CoV-2"
Vaccination against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) results in transient antibody response against the spike protein. The individual immune status at the time of vaccination influences the response. Using mathematical models of antibody decay, we determined the dynamics of serum immunoglobulin G (IgG) and serum immunoglobulin A (IgA) over time. Data fitting to longitudinal IgG and IgA titers was used to quantify differences in antibody magnitude and antibody duration among infection-naïve and infection-positive vaccinees. We found that prior infections result in more durable serum IgG and serum IgA responses, with prior symptomatic infections resulting in the most durable serum IgG response and prior asymptomatic infections resulting in the most durable serum IgA response. These findings can guide vaccine boosting schedules.
4. Grant Lythe University of Leeds
   "Models of bursting and budding"
When are infectious viruses or bacteria released from infected cells? We consider two types of mathematical models. In the first, “budding'', infected cells are assumed to release new infectious particles at a constant rate (that is, constant probability per unit time). No description of the intracellular dynamics is needed; the mean number of new infectious particles released per infected cell is simply the rate of release multiplied by the mean lifetime of an infected cell. In the second, “bursting'', infectious particles accumulate inside a host cell until the cell dies and the intracellular load is released at once. At the stochastic level of an individual cell, the simplest budding models have two types of events (release of an infectious particle and death of the infected cell), and the mathematics is consistent with the assumption that events are independent. In bursting, however, release of infectious particles and death of the host cell are not independent events: they occur simultaneously.

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

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

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

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

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

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

Organized by: Rebecca Crossley, Stéphanie Abo (University of Oxford), University of Oxford

1. John Nardini The College of New Jersey
   "Decoding agent-based model behavior: novel methods for prediction and global sensitivity analysis"
Agent-based models (ABMs) are invaluable tools for studying the emergence of collective behavior in biology. Unfortunately, it is challenging to analyze ABM behavior due to their computational and stochastic nature. In this talk, I will present two recent studies aimed at developing new methodologies to enable the prediction, interpretation, and analysis of ABMs. In the first study, we use biologically-informed neural networks (BINNs) to forecast and predict ABM behavior. In particular, we show BINNs can learn interpretable differential equations to predict ABM data at new parameter values, and demonstrate this success using three case study ABMs of collective migration. In the second study, we combine several machine learning algorithms to develop a global sensitivity analysis pipeline for ABMs that is capable of identifying sensitive parameters, revealing common model patterns, and linking input model parameters to these patterns using a spatial ABM of tumor spheroid growth. Taken together, these studies demonstrate how concepts from machine learning are valuable for studying ABMs and will advance data-driven ABM modeling.
2. Jinchao Feng Great Bay University
   "A Sparse Bayesian Learning Algorithm for Estimation of Interaction Kernels in Motsch-Tadmor Model"
In this talk, we present a data-driven framework for identifying asymmetric interaction kernels in the Motsch–Tadmor model based on observed agent trajectories. Unlike symmetric models, the asymmetric setting introduces a nonlinear inverse problem due to the normalization of interaction weights. We reformulate the problem using the implicit form of the governing equations, reducing kernel learning to a subspace identification task. To solve this, we develop a sparse Bayesian learning approach that incorporates prior structure and quantifies uncertainty, enabling robust model selection under noise. Numerical experiments on several prototype systems demonstrate the method's ability to recover key interaction patterns and predict collective behavior accurately, even with limited or noisy data.
3. Seungwoong Ha Santa Fe Institute
   "Toward a Data-Centric Understanding of Collective Dynamics"
Understanding how collective behavior emerges from local interactions is a central question in modeling biological systems. While traditional approaches often assume fixed interaction rules, recent advances in data-driven modeling offer ways to infer these laws directly from empirical observations. In this talk, I present a set of machine learning-based methods developed to recover interaction structures and underlying dynamics in complex systems, from physical to population-level collective behavior. Across different scenarios, these approaches infer continuous interaction strengths, capture emergent phenomena not present in training data, and remain applicable to stochastic or temporally evolving systems. I will also highlight how adaptive agents can develop robust coordination strategies through learning in uncertain environments. These results suggest new pathways for linking observed dynamics to latent interaction rules, offering complementary tools to classical models of population dynamics.
4. Ming Guo Massachusetts Institute of Technology
   "Collective curvature sensing and fluidity in three-dimensional multicellular systems"
Collective cell migration is an essential process throughout the lives of multicellular organisms, for example in embryonic development, wound healing and tumour metastasis. Substrates or interfaces associated with these processes are typically curved, with radii of curvature comparable to many cell lengths. Using both artificial geometries and lung alveolospheres derived from human induced pluripotent stem cells, here we show that cells sense multicellular-scale curvature and that it plays a role in regulating collective cell migration. As the curvature of a monolayer increases, cells reduce their collectivity and the multicellular flow field becomes more dynamic. Furthermore, hexagonally shaped cells tend to aggregate in solid-like clusters surrounded by non-hexagonal cells that act as a background fluid. We propose that cells naturally form hexagonally organized clusters to minimize free energy, and the size of these clusters is limited by a bending energy penalty. We observe that cluster size grows linearly as sphere radius increases, which further stabilizes the multicellular flow field and increases cell collectivity. As a result, increasing curvature tends to promote the fluidity in multicellular monolayer. Together, these findings highlight the potential for a fundamental role of curvature in regulating both spatial and temporal characteristics of three-dimensional multicellular systems.

Organized by: Kang-Ling Liao (University of Manitoba), Wenrui Hao, Pennsylvania State University

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

1. Kang-Ling Liao University of Manitoba
   "Mathematical Modeling of Breast Cancer Treatment with Radiation, Anti-estrogen, and Immune Checkpoint Inhibitor"
Radiotherapy (RT) and endocrine therapy (ET) are standard treatments for estrogen receptor-positive (ER+) breast cancer, but they could induce resistance and relapse issues. Immune checkpoint inhibitor (ICI) is another potential treatment for breast cancer, but its response rate is low. In this work, we create a system of ordinary differential equations to investigate the combination treatments among RT, ET, and ICI in ER+ breast cancer. Our model quantitatively captures the tumor growth data under the combination among these three treatments for different ER+ breast cancer cell lines. Our numerical predictions indicate that: (i) potential treatment to reduce the relapse caused by RT; (ii) potential breast cell lines have a better response rate to anti-PD-1; (iii) Tumor elimination and no relapse could appear in the combination of RT and ET in MCF-7 ER+ tumor cells; (iv) these treatments have induce better tumor reduction is which breast cancer cell lines. We also study the distribution of parameter values calibrating to different ER+ breast cancer cell lines to categorize (virtual) cohort patients and to provide potential biomarkers for selecting appropriate treatment for patients
2. Tracy Stepien University of Florida
   "Modeling Tumor-Immune Interactions in the Glioblastoma Microenvironment"
Glioblastoma (GBM) is an aggressive brain tumor that is extremely fatal with no current treatment options available that can achieve remission. One potential explanation for minimally effective treatments is due to the characteristically high immune-suppressive glioma microenvironment. We develop an agent-based model to simulate the interactions of glioma cells, T cells, and myeloid-derived suppressor cells (MDSCs) and the effects of oxygen, a T cell chemoattractant, and an MDSC chemoattractant. To validate our model and quantify cell clustering patterns in GBM, we use spatial statistics comparing simulations to data extracted from cross-sectional tumor images of cellular biomarkers.
3. Wenrui Hao Pennsylvania State University
   "Data-Driven Modeling in Alzheimer's Disease"
Alzheimer’s disease (AD) presents complex, nonlinear progression patterns driven by heterogeneous biomarker dynamics, spatial brain changes, and individual variability. Capturing these intricate dynamics requires modeling tools that are both expressive and computationally efficient. In this work, we introduce a Laplacian Eigenfunctions Neural Operator (LENO) framework for data-driven modeling of Alzheimer’s disease. By projecting the underlying spatial-temporal dynamics onto a basis of Laplacian eigenfunctions, LENO exploits the geometric structure of the brain while learning the nonlinear operator governing disease progression. Trained on multi-modal longitudinal data—including neuroimaging, biomarker profiles, and cognitive assessments—our approach enables efficient approximation of disease trajectories and identification of multiple progression pathways. The model not only achieves high predictive accuracy but also reveals interpretable spatial patterns aligned with known AD pathology. LENO provides a powerful computational tool for building digital twins of AD patients, supporting personalized diagnosis, subtyping, and forecasting of disease evolution.
4. Negar Mohammadnejad University of Alberta
   "Strategies for Optimizing the Efficacy of Oncolytic Virus–Immune System Interactions"
Oncolytic virotherapy (OVT) is an innovative cancer treatment in which oncolytic viruses are introduced into a patient to selectively target and destroy tumor cells. In the absence of these viruses, tumors are known to create an immunosuppressive environment. However, upon administration of oncolytic viruses and initiation of virotherapy, the immune system is activated, leading to a robust anti-tumor response. Despite this, oncolytic viruses alone have rarely been shown to induce complete and sustained regression of established tumors in vivo. In this talk, I will discuss key strategies for enhancing the efficacy of oncolytic virotherapy. These include the integration of immunotherapy approaches with virotherapy to amplify anti-tumor immune responses, as well as optimizing the timing, dosage, and sequencing of viral administrations to maximize therapeutic benefits. By refining these strategies, we aim to improve treatment outcomes and potentially enhance the therapeutic impact of oncolytic virotherapy.

Organized by: Sydney Ackermann, Ramanarayanan Kizhuttil, Samrat Sohel Mondal (Wodarz lab) (University of California, San Diego)

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

Organized by: Dhananjay Bhaskar (Yale University), Bernadette Stolz-Pretzer

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

1. Katherine Benjamin University of Oxford
   "Topological methods for subcellular spatial transcriptomics"
Spatial transcriptomics technologies produce gene expression measurements at millions of locations across a tissue sample. An open problem in this area is the inference of spatial information about single cells. Here we present a multiscale machine learning method to pinpoint the locations of individual sparsely dispersed cells from subcellular spatial transcriptomics data. We integrate this approach with multiparameter persistence landscapes, a state of the art tool in topological data analysis, to identify a loop structure in infiltrating glomerular immune cells in a mouse model of lupus nephritis.
2. Veronica Ciocanel Duke University
   "Unraveling aster and ring structures in cell models of dynamic actin filaments using topological data analysis"
Actomyosin is a dynamic network of interacting proteins that reshapes and organizes in a variety of structures that are essential in cell movement, cell division, as well as in wound healing. Agent-based models can simulate realistic dynamic interactions between actin filaments and myosin motor proteins inside cells. These stochastic simulations reproduce bundles, clusters, and contractile rings that resemble biological observations. We have developed techniques based on topological data analysis to extract insights from spatio-temporal data in these protein network interactions. Recently, we have been interested in adapting the framework of vines and vineyards in order to track topological and geometrical features through time-parameterized stacks of persistence diagrams. This approach allows us to quantify characteristics of formation and maintenance of relevant actin structures such as rings and asters in simulated datasets. This is joint work with Niny Arcila-Maya.
3. Robert McDonald University of Oxford
   "Topological model selection: a case-study in tumour-induced angiogenesis"
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data. Approximate Bayesian Computation is a widely-used method for parameter inference and model selection in such scenarios, and it may be combined with Topological Data Analysis to study models which simulate data with fine spatial structure. We develop a flexible pipeline for parameter inference and model selection in spatio-temporal models. Our pipeline identifies topological summary statistics which quantify spatio-temporal data and uses them to approximate parameter and model posterior distributions. We validate our pipeline on models of tumour-induced angiogenesis, inferring four parameters in three established models and identifying the correct model in synthetic test-cases.
4. Nan Wu University of Texas at Dallas
   "Adaptive Bayesian regression on manifold"
We investigate how the posterior contraction rate under a Gaussian process prior is influenced by the intrinsic dimension of the domain and the smoothness of the regression function. Specifically, we consider the setting where the domain is a d-dimensional manifold and the regression function is intrinsically s-Hölder smooth on the manifold. We establish the optimal posterior contraction rate of O(n^{-s/(2s + d)}), up to a logarithmic factor. To eliminate the need for prior knowledge of the manifold's dimension, we propose an empirical Bayes prior on the kernel bandwidth, leveraging kernel affinity and k-nearest neighbor statistics. This talk is based on joint work with Tao Tang, Xiuyuan Cheng, and David Dunson.

Organized by: Changhan He (University of California, Irvine), Chengyue Wu, University of Texas MD Anderson Cancer Center

1. Lifeng Han Tulane University
   "Calibrate a phenotype-structured population model with cell viability data to study drug resistance in cancer treatment"
We fit a phenotype-structured population mode to cell viability data on a drug used for ovarian cancer, olaparib. This approach reveals the effects of a drug on fitness landscape and the evolution of a population of cancer cells structured with a spectrum of drug resistance. We will show that maximizing variation in plasma drug concentration over a dosing interval could be important in reducing drug resistance. We will discuss the potential use of this model to design drug treatment regimens to improve cancer treatment.
2. Wenjun Zhao Wake Forest University
   "Dynamical GRN inference via optimal transport"
In this talk, we present a framework for inferring gene regulatory networks from time-stamped single-cell gene expression data. Our algorithm first reconstructs the correspondence between single cells across time points through optimal transport, and then infers the underlying dynamical model governing gene expression dynamics, which can be interpreted in terms of differential equations. We will also discuss extensions of this framework to infer context-specific regulatory mechanisms.
3. Qixuan Wang University of California, Riverside
   "Hair follicle cell fate regulations and the effect on the follicle growth control"
In tissues, proper regulations of cell fate decisions are important in maintaining the shape and functions of the tissue. In this talk, I will present our recent research in modeling cell fate regulation mechanisms, using mammalian hair follicles as a model system. Hair follicles are mini skin organs, and they are highly dynamic in the way that they can undergo cyclic growth during the lifespan of the organism. To maintain tissue homeostasis and functions of a hair follicle, the follicle transient amplifying epithelial cells need to make correct decisions among cell division, differentiation and apoptosis, instructed by various signals produced by the follicle itself as well as by the surrounding skin environment. We develop a probabilistic Boolean model based on both literature and published single-cell RNA sequencing data. Using both computational simulations and attractor analysis, we investigate how hair follicle epithelial cells respond to TGF-beta, BMP and TNF, so to make the correct cell fate decision, and how signals cooperatively regulate hair follicle growth dynamics. Next, we develop a hybrid multiscale model on the bottom part of a HF, and use it to investigate how signaling dynamics, cellular kinetics and movement, and gene regulation coordinate to regulate the HF cell fate decisions in the tissue.
4. Axel Almet University of California, Irvine
   "Systems modeling of cellular senescence using single-cell transcriptomics"
Cellular senescence is a stress-induced cell state characterised by irreversible cell cycle arrest and an enhanced secretome where senescent cells secrete an array of inflammatory signals and remodeling factors. An accumulation of senescent cells across biological age is hypothesised to contribute to aging-related declines in tissue. However, there are contexts where senescent cells may be transiently beneficial. To study the impact of cellular senescence requires a systems approach that analyzes both its intrinsic features, driven by changes in gene transcription dynamics, and its extrinsic impacts on the tissue environment driven by cell-cell communication. Single-cell transcriptomics, which profile molecular states with broad gene coverage and cell type coverage, provide an exciting opportunity to generate further insight into the multi-dimensional features of cellular senescence. In this talk, we present our recent work on using single-cell transcriptomics to dissect the multi-dimensional features of cellular senescence. First, we fit stochastic models of gene transcription to ground truth single-cell RNA-sequencing datasets of cellular senescence to dissect how cellular senescence drives intrinsic changes in gene transcription kinetics. We then shift our analysis to the perspective of cell-cell communication, identifying senescence-driven communication modules that can reveal novel senescent cell states with distinct communication patterns and, in turn, show how these communication patterns are associated with distinct transcriptional features. Overall, these analyses reveal new ways that we can integrate sequencing data and mathematical modeling to better understand cellular senescence.

Organized by: Einar Bjarki Gunnarsson (Science Institute, University of Iceland), Maximilian Strobl (Cleveland Clinic, USA, stroblm@ccf.org)

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

1. Einar Bjarki Gunnarsson Science Institute, University of Iceland
   "Decoding drug-induced persistence: Integrating theory with experiments and optimizing dosing protocols"
Drug resistance is a common reason for treatment failure in cancer. While resistance evolution is usually viewed through the Darwinian lens of random mutation and selection, mounting evidence indicates that anti-cancer drugs designed to kill tumor cells can simultaneously induce the adoption of non-genetic drug-persistent cell states. This confounds conventional high-dose treatment strategies aimed at maximal tumor reduction, since high doses can simultaneously accelerate the evolution of resistance. At the same time, the reversible nature of non-genetic mechanisms creates opportunities for delaying resistance evolution through intermittent or adaptive therapy. In this talk, we discuss mathematical modeling of drug-induced persistence and its role in the evolution of stable drug resistance. We also discuss how mathematical modeling can be used to derive optimal drug schedules aimed at maximally delaying tumor recurrence. In doing so, we introduce the central conversation of the mini-symposium involving the integration of mathematical modeling with experimental data, which we believe is crucial to achieve the long-term goal of personalized model-informed optimal drug scheduling.
2. Mattia Corigliano IFOM - The AIRC Institute of Molecular Oncology, Milan, Italy
   "Optimal treatment for drug-induced cancer persisters involves release periods and intermediate drug doses"
Targeted cancer therapies often induce a reversible drug-tolerant state in subpopulations of cells, akin to bacterial persistence. Precise characterization of these 'cancer persisters' is crucial for designing more effective treatment strategies. Our recent work demonstrates that, unlike bacterial systems, the transition to persistence in colorectal cancer cell lines exhibits a distinct dependence on drug presence and concentration. In this talk, I will present a mathematical modeling framework that leverages these findings to explore intermittent treatment protocols aimed at reducing the long-term fitness of the treated population. By adapting a bacterial persistence model to colorectal cancer dynamics, we identify success and failure regions within a clinically accessible parameter space. Strikingly, our analysis suggests that optimal treatment outcomes may be achieved with non-zero recovery periods and drug concentrations lower than those typically administered in clinics. Moreover, incorporating patient drug pharmacokinetics into the model reveals that intermittent dosing strategies, currently explored in clinical trials, can be optimized to potentially rival the efficacy of continuous treatment regimens. These results highlight the power of mathematical modeling in optimizing cancer treatment protocols, offering insights into non-trivial trade-offs that could improve patient outcomes.
3. Irina Kareva Northeastern University
   "Dosing Strategies for Bispecifics with a Bell-Shaped Efficacy Curve: What Looks Like Resistance May Be Corrected Through Schedule Adjustments"
Bispecific T cell engagers (TCEs) can exhibit bell-shaped efficacy curves, where increasing the dose beyond a certain point leads to reduced, not improved, efficacy. This counterintuitive behavior arises when efficacy depends on forming a trimeric complex between drug, tumor target, and T cell receptor, as is the case with teclistamab, a bispecific targeting BCMA and CD3 in multiple myeloma. Using a semi-mechanistic PK/PD model and a virtual patient population, we demonstrate that apparent loss of response may reflect overdosing rather than true resistance. We explore how measurable pre-treatment biomarkers, such as soluble and membrane-bound BCMA, can guide dose optimization and patient stratification. The model supports a shift toward semi-personalized dosing strategies and highlights that lowering the dose may, in some patients, restore efficacy.
4. Tatiana Miti Moffitt Cancer Center & Research Institute
   "ABM studies on the role of the drug-sheltering effects of stroma on the emergence of resistance"
Lung cancer is the leading cause of cancer-related deaths in the U.S., with non-small cell lung cancer (NSCLC) accounting for 84% of cases and a low 5-year survival rate of 6%. About 20% of NSCLC cases involve abnormal activation of receptor tyrosine kinases, which are treated with tyrosine kinase inhibitors (TKIs). Unfortunately, despite the magnificent initial results, TKIs show modest outcomes as tumors evolve, gain resistance, and eventually relapse. Experimental data suggest that drug-resistant tumor subpopulations emerge after TKI treatment through de novo mutations and epigenetic changes. In vitro studies indicate that this adaptation is supported by microenvironmental factors, particularly cancer-associated fibroblasts (CAFs), which protect tumor cells via secreted paracrine factors, hence access to these pro-survival factors depends on the spatial organization of tumors. However, despite the massive body of studies, the exact contribution of stromal protection to the minimal residual disease and ultimate relapse remains unknown. Based on published data from other teams, as well as published and unpublished data from Dr. Marusyk’s lab we use an Agent-Based Model to assess the stromal effects on the remission-relapse dynamics if (1) CAF mediated stromal protection effects only those tumor cells that are located at close proximity to stroma, (2) both total amount and spatial patterns of stroma within tumors are varied and (3) CAF mediated stromal protection reduces the initial drug induced tumor cell elimination yielding the accumulation of epigenetic mutations, thus contributing to the residual disease and preserving intratumor heterogeneity. Our results show that using mathematical models, we can gain a deeper understanding of the ecological mechanisms that lead to NSCLC relapse under TKI treatment and uncover new therapeutic strategies that account for stromal effects and successfully eradicate tumors.

Organized by: Andrew Eckford (Department of Electrical Engineering and Computer Science, York University, Toronto)

1. Massimiliano Pierobon University of Nebraska-Lincoln
   "On the Usefulness and Subjectivity of Life-supporting Information"
In recent years, the exploration of information flow within biological systems has become a groundbreaking approach for delving into the complex mechanisms at play in the life sciences. This approach serves a dual purpose: it not only provides a quantitative grasp of how biological systems store, transmit, sense, receive, and process information across various scales and contexts, but it also paves the way for designing and engineering systems that either mimic or are integrated with biochemical environments. At this interdisciplinary juncture, bridging the gap between diverse fields of expertise presents numerous challenges. These range from developing a shared vocabulary to addressing the limitations of applying theories and concepts across different contexts and assumptions. In our talk, we will share insights and lessons from organizing the Workshop on Information, Communication, and Coding Theory in Biology sponsored by the US National Science Foundation. We'll highlight cutting-edge interdisciplinary research areas and the major challenges that lie ahead. Our discussion will then delve into our research contributions, focusing on how communication theory can accurately describe biological processes and introducing the concept of subjective information as a new metric for biological information. We will also present practical applications derived from our research, offering recommendations for best practices and sharing personal anecdotes from our journey. This talk aims to illuminate the path forward for interdisciplinary collaboration in understanding and harnessing the principles of information flow in biological systems.
2. Alexander Moffett Northeastern University
   "Evolution of Environmental Sensing"
Organisms sense and respond to environmental cues, allowing for within-lifetime adaptation to an ever-changing world. A growing body of work has sought to connect the accuracy of environmental sensing with fitness, with the fitness value of information emerging as a key concept. Despite the progress made in this direction, we still lack a good understanding of how environmental sensing evolves in necessarily finite populations with metabolically costly sensory machinery. We attempt to construct a model capable of addressing these gaps in understanding, using concepts from rate-distortion theory and population genetics.
3. Andrew Eckford York University
   "Kelly Bets and Single-Letter Codes: Optimal Information Processing in Natural Systems"
In an information-processing investment game, such as the growth of a population of organisms in a changing environment, Kelly betting maximizes the expected log rate of growth. In this talk, we show that Kelly bets are closely related to optimal single-letter codes (i.e., they can achieve the rate-distortion bound with equality). Thus, natural information processing systems with limited computational resources can achieve information-theoretically optimal performance. We show that the rate-distortion tradeoff for an investment game has a simple linear bound, and that the bound is achievable at the point where the corresponding single-letter code is optimal. Moreover, since evolution is expected to optimize an organism's information processing capabilities, this bound allows prediction of biological behaviour. Examples illustrating the results in simplified biological scenarios are presented.
4. Peter Thomas Case Western Reserve University
   "Tradeoffs in the energetic value of neuromodulation in a closed-loop neuromechanical system"
Rhythmic motor behaviors controlled by neuromechanical systems, consisting of central neural circuitry, biomechanics, and sensory feedback, show efficiency in energy expenditure. The biomechanical elements (e.g., muscles) are modulated by peripheral neuromodulation which may improve their strength and speed properties. However, there are relatively few studies on neuromodulatory control of muscle function and metabolic mechanical efficiency in neuromechanical systems. To investigate the role of neuromodulation on the system’s mechanical efficiency, we consider a neuromuscular model of motor patterns for feeding in the marine mollusk Aplysia californica. By incorporating muscle energetics and neuromodulatory effects into the model, we demonstrate tradeoffs in the energy efficiency of Aplysia’s rhythmic swallowing behavior as a function of the level of neuromodulation. A robust efficiency optimum arises from an intermediate level of neuromodulation, and excessive neuromodulation may be inefficient and disadvantageous to an animal’s metabolism. This optimum emerges from physiological constraints imposed upon serotonergic modulation trajectories on the energy efficiency landscape. Our results may lead to experimentally testable hypotheses of the role of neuromodulation in rhythmic motor control.

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-1.

1. Fanze Kong University of Washington
   "Spike Dynamics in Several Keller-Segel Models with Logistic Growth"
The Keller–Segel models, a class of strongly coupled PDEs, were introduced by E. Keller and L. Segel in the 1970s to describe cell motility driven by chemical signals. Due to their relatively simple structures yet rich dynamical behaviors, Keller–Segel systems have attracted extensive attention, with numerous studies devoted to the qualitative properties of the solutions, including global well-posedness, singularity formation, etc. This talk focuses on the localized pattern formation in several Keller-Segel models with logistic growth, where two singular limit regimes are considered: large chemotactic movement and small chemical diffusivity. We will show the results concerning the existence and stability of multi-spikes. Furthermore, some complex but intriguing spike dynamics including oscillation, slow motion and nucleation will be discussed. In particular, we highlight the connection between logistic Keller–Segel and Gierer–Meinhardt models, and discuss the application of logistic Keller-Segel models to explaining economic agglomeration.
2. Mohammad El Smaily University of Northern British Columbia
   "A Wol­bachia infec­tion mod­el with free bound­ary"
We develop a reaction-diffusion model, with free-boundary, to describe how Wolbachia can be used to eliminate mosquitoes that spread human disease. The mosquito population infected with Wolbachia invades the environment with a spreading front governed by a free boundary satisfying the well-known one-phase Stefan condition. We establish criteria under which spreading and vanishing occur. Our results provide useful insights on designing a feasible mosquito releasing strategy that infects the whole mosquito population with Wolbachia and eradicates the mosquito-borne diseases eventually.
3. Michael Ward University of British Columbia
   "Diffusion-Induced Synchrony for a Cell-Bulk Compartmental Reaction-Diffusion System in 3-D"
We investigate diffusion induced oscillations and synchrony for a 3-D PDE-ODE bulk-cell model, where a scalar bulk diffusing species is coupled to nonlinear intracellular reactions that are confined within a disjoint collection of small spheres. The bulk species is coupled to the spatially segregated intracellular reactions through Robin conditions across the boundaries of the small spheres. For this system, we derive a new memory-dependent ODE integro-differential system that characterizes how intracellular oscillations occur in the collection of cells are coupled through the PDE bulk-diffusion field. By using a fast numerical approach relying on the ``sum-of-exponentials'' method to derive a time-marching scheme for this nonlocal system, diffusion induced synchrony is examined for various spatial arrangements of cells. This theoretical modeling framework, relevant to applications such as quorum sensing when spatially localized nonlinear oscillators are coupled through a PDE diffusion field, is distinct from the traditional Kuramoto paradigm for studying oscillator synchronization through ODEs coupled on networks or graphs. (Joint work with Merlin Pelz, UBC and UMinnesota).
4. Shuangquan Xie Hunan University
   "Spiky patterns and their dynamics in a three-component food chain system"
We study a three-component reaction-diffusion system modeling interactions among water (resource), vegetation (primary consumer), and a predator (secondary consumer). The water-vegetation dynamics follow Klausmeier-type kinetics, while the vegetation-predator interaction incorporates logistic growth with nonlinear predation. This framework captures scenarios like arid ecosystems (water-limited vegetation) with predator-driven vegetation suppression. We asymptotically construct spiky spatial solutions in certain parameter regimes and demonstrate that these solutions undergo Hopf bifurcations due to translational instability.