Special Session 24: Mathematical and Computational Modeling of Complex Biological Systems

An immuno-epidemiological model with consideration for symptom score

Summer Atkins The University of Alabama in Huntsville USA Co-Author(s):    Summer Atkins (The University of Alabama in Huntsville), Binod Pant (Northeastern University), and Hana Dobrovolny (Texas Christian University)

Abstract: The incorporation of human behavior into epidemiological modeling has been quite a popular topic as of late, and there are many effective ways to mathematically introduce behavior into such models. In this talk, we incorporate behavior into an epidemiological model for an upper respiratory infectious disease based upon an assumption that the sicker an individual feels the more likely they will reduce their contacts. Our methodology in capturing this behavioral assumption will be through a nested-multiscale modeling approach. The within-host dynamics of a symptomatic individual is represented by a system of ordinary differential equations in which one of the compartments measures the symptom score of the infected individual. This model is then linked to an age-structured between-host model (where age represents time since infection) by having a reduction in contact rate be a function that depends on the individual`s symptom score. In this talk, we present a flowchart of the model, some of the analytical results, and some simulations. In our simulations, we vary parameters of the linking function to investigate how the transmission dynamics change based on how reactive an individual is to their symptoms.

On the influence of diffusion strategies on the average population levels and competition outcomes

Elena Braverman University of Calgary Canada Co-Author(s):    Andr\`{e} Rickes, Jennifer Lawson

Abstract: In 2006, Lou proved that, once the intrinsic growth rate $r$ in the logistic model is proportional to the spatially heterogeneous carrying capacity $K$ ($r=K^1$), the total population under the regular diffusion exceeds the total of the carrying capacity. DeAngelis et al (2016) argued that the prevalence of the population over the carrying capacity is only observed when the growth rate and the carrying capacity are positively correlated, at least for slow dispersal. Guo et al (2020) justified that, once $r$ is constant ($r=K^0$), the total population is less than the cumulative carrying capacity. Together with filling up the gap for when $r=K^{\lambda}$ for any real $\lambda$, we define a diffusion strategy as the tendency to have a distribution proportional to a certain positive prescribed function, once a diffusion coefficient grows infinitely, and explore the interplay of harvesting and dispersal strategies and their influence on the outcome of the competition for two resource-sharing species. While achieving extinction by excessive culling of the undesired species is simple and efficient, keeping biodiversity is a more complicated task. Proposing such heterogeneous harvesting that the two populations become an ideal free pair allows to guarantee coexistence.

Awareness and compliance in an infectious disease model

Jacques B\\'{e}lair Universit\\\\\\\\\\\\\\\\'{e} de Montr\\\\\\\\\\\\\\\\'{e}al Canada Co-Author(s):

Abstract: Management of the COVID-19 pandemic required in its early stages the deployment of non pharmaceutical interventions (NPIs) [social isolation, physical distancing, mask-wearing, hand-washing]. We consider a compartmental model of disease propagation in which information is the infection: knowledge of, and compliance with, measures limiting the propagation of an infectious disease (such as non-pharmaceutical interventions (NPIs)) are modeled as dynamic parameters. The population is divided in three classes: unaware individuals, aware but noncompliant and aware and compliant individuals so that the model takes the form, in its simplest form, of the equations \[ \left\{ \begin{array}{ll} S_0'(t) &= \mu -\beta A S_0 -\mu S_0\ S_1(t) &=  (1-p)\beta S_0 A - \beta S_1 A-\mu S_1 +\gamma(A) A\ A'(t) &= \beta (pS_0+S_1)A-(\mu +\gamma(A))A \end{array} \right. \] Conditions for the existence of multiple stable equilibria will be discussed as well as the consequences for the control of the infection.

Some dimension reduction techniques for Leslie matrix models

Troy Day Queen`s University Canada Co-Author(s):    Amy Forsythe, Sarah Otto

Abstract: Leslie matrix projection models have long served as powerful tools for tracking populations and their age structure over time. One of their main appeals is the simplicity that arises from grouping individuals into age classes in which all individuals have the same vital rates. Nevertheless, in natural populations many traits influence survival and reproduction and so real-world age groups are composed of a heterogeneous mix of individuals with different vital rates. This heterogeneity is sometimes accounted for in models by expanding the Leslie matrix to include multiple phenotypic classes within each age category; however, it becomes increasingly difficult to analyze these matrices as the dimension increases. Here, we present 3 theorems about when and how projection matrices for populations structured by both age and phenotypic classes can be collapsed to smaller and more easily evaluated matrices while preserving the general solution of the original model.

A nonlocal advection system for two competing species with resources recovering time

Yoichi Enatsu Tokyo University of Science Japan Co-Author(s):    Ping Zeng, Guanyu Zhou

Abstract: We investigate the nonlocal advection model for two-species competition, which characterizes cell growth and dispersion phenomena in co-culture experiments. To capture realistic phenomena in biology, we introduce the time delay representing population migration and resources recovering time. We investigate the impact of delays on competitive dynamics and to develop numerical methods that ensure biological feasibility of solutions. Accordingly, we design a positivity-preserving finite volume scheme based on an upwind flux approach, guaranteeing non-negative population densities and discrete conservation properties. We examine the convergence orders of the scheme through the numerical experiments and explore the effects of delays on species competition dynamics.

The transmission of chikungunya in Guangdong China in 2025

Daihai He The Hong Kong Polytechnic University Hong Kong Co-Author(s):

Abstract: The mosquito-borne infection chikungunya hit Guangdong China in 2025. We propose and fit an epidemic model to the chikungunya reported cases from four hit hardest cities in Guangdong. We analyze mosquito surveillance data from Guangzhou. We assume a unified reporting ratio across cities and over time. We reveal huge temporal changes in transmission rate, which might be due to huge changes in reporting effort in Jiangmen and Foshan. We find the infection attack rates are very different across cities. If we instead assume similar level of infection attack rates across cities, then the reporting ratio must be very different between cities. We also analyze the correlations between transmission rates and environmental factors and mosquito data. But given the short time period, these correlations should be taken with caution.

From Viral Kinetics to Epidemic Dynamics: A Unified Multiscale Modeling Framework with Analytical and Agent-Based Approaches

Byul Nim Kim Kyung Hee University/Department of Applied Mathematics Korea Co-Author(s):    Hyosun Lee, Sunmi Lee

Abstract: We develop a unified multiscale modeling framework that integrates within-host viral kinetics with population-level epidemic dynamics, combining analytical and agent-based approaches. Motivated by SARS-CoV-2 variant evolution, we first construct a mechanistic SEIIRS-renewal model in which infection-age-dependent infectiousness is derived from viral load trajectories through a nonlinear Hill-type mapping. This formulation enables rigorous analytical characterization of epidemic thresholds, including a kernel-based basic reproduction number, Euler--Lotka growth rates, and explicit conditions for backward bifurcation induced by waning immunity and reinfection. To complement this theoretical framework, we develop a multi-scale agent-based model that embeds empirically inferred viral kinetics into network-based transmission dynamics. By mapping individual viral load trajectories to time-varying transmission probabilities, the model captures heterogeneous contact structures and stochastic transmission processes, allowing for realistic simulation of variant-specific epidemic patterns. Our results demonstrate that differences in viral replication and clearance fundamentally reshape epidemic dynamics, even under identical reproduction numbers. Fast-replicating variants generate earlier and sharper epidemic peaks, whereas slower viral dynamics lead to delayed but more prolonged outbreaks. The integration of within-host kinetics further produces heterogeneous transmission patterns and heavy-ailed secondary infection distributions without imposing ad hoc assumptions. Together, the proposed framework establishes a coherent bridge from biological mechanisms to population-level outcomes, providing both analytical insight and computational tools for understanding variant-specific transmission dynamics. This unified multiscale approach offers a flexible foundation for epidemic forecasting, risk assessment, and timing-sensitive intervention design in emerging infectious diseases.

THE FIRST MATHEMATICAL MODEL FOR ELK-WOLF INTERACTION IN YELLOWSTONE NATIONAL PARK USING E-SINDY ALGORITHM

Nitu Kumari IIT Mandi India Co-Author(s):

Abstract: The ecological dynamics between elk and wolves in northern Yellowstone have been a focal point of long-term research, particularly following the reintroduction of wolves to the region. Although numerous studies have explored this prey-predator interaction from ecological and behavioral perspectives, there remains a lack of comprehensive analysis using mathematical modeling approaches capable of uncovering underlying dynamical patterns and system-level insights. In this study, we investigate the prey-predator dynamics of the elk--wolf system in northern Yellowstone National Park, USA, using a data-driven modeling approach. We used yearly population data for elk and wolves from 1995 to 2022 (28 years) to construct a mathematical model using a sparse regression modeling framework. To the best of our knowledge, no previous work has applied this framework to capture elk--wolf interactions over this time period. Our modeling pipeline integrates Gaussian process regression for data smoothing, sparse identification of nonlinear dynamics for model discovery, and model selection techniques to identify the most suitable mathematical representation. The resulting model is analyzed for its non-linear dynamics with ecologically meaningful parameters.

Modeling for a purpose: an influenza outbreak in a boarding school revisited.

Michael Li University of Alberta Canada Co-Author(s):

Abstract: Assessment of models should depend on the modeling objectives. Models that incorporate more realistic mechanisms are more suitable for providing insights. To produce reliable and accurate predictions and inform public health decision making, parsimonious models are more appropriate and the modeling needs to respect the data. Most of all, model calibration results should be validated by data that is independent of the calibration data, before scenario analysis is made to inform policy. As a case study, we revisit the well-known example of a 1978 influenza outbreak in a boarding school in England. We demonstrate that a parsimonious SIR model with data informed time-dependent parameters can produce both accurate fitting to the time series data and validation by the final size of the epidemic. Furthermore, modeling results also provide evidence of the likely epidemic control measures implemented at the school.

Infectious disease surveillance using deep learning models

Bouchra BN NASRI University of Montreal Canada Co-Author(s):

Abstract: Social media data has become widely used to monitor infectious diseases. This presentation will showcase case studies of social media data related to Mpox and Lyme disease, demonstrating the utility of such data in predicting cases and other disease-related characteristics.

Catastrophic changes in coral reef dynamics under macroalgal toxicity, elevated sea surface temperature (SST), overfishing and invasion of predators

Samares Pal University of Kalyani India Co-Author(s):

Abstract: Coral reef ecosystems are most vulnerable to changes in sea surface temperature (SST), a key environmental factor critical to reef-building growth. Elevated SST reduces the ability of corals to produce their calcium carbonate skeletons. Prolonged high SST results in coral bleaching owing to the uncoupling of symbiosis among corals and microalgae. Corals have narrow temperature tolerances. The skeletal growth rate of corals falls sharply to zero even at a slight increase of SST above its temperature tolerance level. Corals are also vulnerable to macroalgal toxicity. Several benthic macroalgae species are known to bring about allelopathic chemical compounds that are very harmful to corals. The toxic-macroalgae produce allelochemicals for which the survivability and settlement of coral larvae are highly affected. Toxic macroalgae species damage coral tissues when in contact by transferring hydrophobic allelochemicals present on macroalgal surfaces, leading to a reduction of corals and even coral mortality. The abundance of toxic macroalgae changes the community structure towards a macroalgae-dominated reef ecosystem.

Modeling Climate-Driven Spatiotemporal Mosquito Population and Dengue Risk

Naveen K. Vaidya San Diego State University USA Co-Author(s):

Abstract: Dengue fever is a vector-borne viral disease primarily transmitted by Aedes mosquitoes. Both population structure and dengue transmission are highly influenced by climate conditions. In this talk, I will present a dynamical system model and a math-model-informed neural network (MINN) based method to predict climate-driven spatiotemporal dynamics of mosquito populations. Furthermore, I will develop a hybrid probabilistic-mechanistic, data-driven model that enables us to estimate a practical, local-level risk of dengue infection. We use data from Nepal, which provides a valuable setting for dengue modeling due to its strong spatial heterogeneity; its 77 districts span a wide range of elevation and climate zones. We analyze our model to formulate reproduction numbers that determine the global dynamics of mosquito survival. Our method identifies the climate conditions that help control dengue-transmitting mosquitoes. Our results provide critical insights into the role of climate change in shifting the distribution of dengue-transmitting mosquitoes and related epidemics into colder regions. Our model`s real-time risk assessment provides an evidence-based methodology for designing public health policies.

Cognitive Movement Strategies in a Resource-Threat Dilemma

Tianxu Wang university of Alberta Canada Co-Author(s):    Jiwoon Sim, Hao Wang

Abstract: Dilemmas involving trade-offs between acquiring food and avoiding threats are unavoidable in animals` daily lives. To enhance survival, they must continually adjust their movement in response to environmental cues, while internal hunger levels also strongly influence their decision-making processes. In this study, we develop a general coupled PDE--ODE model that integrates movement strategies driven by internal hunger dynamics. Even in the same environment, different species may prioritize different types of information. We investigate how various cognitive movement strategies affect species` survival outcomes in simplified food--threat dilemmas. Specifically, we compare five commonly observed strategies based on local gradients, regional maxima, global maxima, regional aggregate gradients, and global aggregate gradients. We prove the well-posedness of the model, in which a general function of the ODE variable appears in the taxis sensitivity function in the PDE equation, and we conduct a stability analysis around arbitrary equilibria. These results are then used to determine survival and extinction conditions under each strategy. Numerical simulations show that the effectiveness of movement strategies strongly depends on environmental context. The global-maximum strategy yields the greatest survival with minimal foraging and threat-avoidance effort in a simple dilemma, while in more complex multimodal environments, local strategies produce the highest population survival rate.

Modeling and Analysis of Legionnaries` Disease

Lihong Zhao Kennesaw State University USA Co-Author(s):

Abstract: Some pathogens can survive and replicate in abiotic environment outside the host systems and rely on the interaction with an environmental reservoir to transmit and infect hosts. Mathematical modeling can provide insights into the complex and often unknown dynamics of environmentally transmitted diseases. One such disease is Legionnaries` disease (LD), an atypical pneumonia caused by the inhalation of the intracellular bacterium Legionella pneumophila suspended in aerosolized water. Reported LD cases have been increasing since the early 2000s, with nearly 10,000 LD cases were reported in the United States. LD remains underdiagnosed and underreported; therefore, its true incidence is unknown. In this talk, I will present the models we developed to examine the factors that may have contributed to the increase in LD outbreaks, and the insights into management strategies using control theory.