MS05 - MEPI-08 Part 3 of 3

Modeling Complex Adaptive Systems in Life and Social Sciences (Part 3)

Wednesday, July 16 from 10:20am - 12:00pm in Salon 8

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

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

Description:

Utilizing complex adaptive systems in modeling has proven to be a powerful approach for understanding various aspects of life and social sciences across spatial and temporal scales. This special session will bring together a distinguished and diverse group of scholars from mathematics, biology, ecology, and epidemiology. These experts apply mathematical models and theoretical analysis to gain insights into critical biological, epidemiological, and social challenges. The session aims to provide an effective platform for presenting and discussing the latest research, fostering collaboration among professionals from different universities and career stages. Our goal is to encourage a rich exchange of ideas by assembling a group of researchers with diverse backgrounds, with a particular emphasis on promoting minority representation. The invited speakers span institutions across multiple countries and include individuals at various career stages, from early-career researchers to senior scholars. This inclusive approach ensures equal opportunities for all participants to present their findings and engage in meaningful collaborations.

Room assignment: Salon 8

Matthew Wheeler

University of Florida

"Linking Network Architecture to Dynamic Behavior"

Modularity is a key feature of biological systems that is well accepted and studied in biology. However, from a mathematical standpoint, it remains poorly defined. In previous work, we developed a decomposition theory based on feedback loops, linking network structure to the organization of its dynamics. We went on to propose that an appropriate definition for a module of a network are the irreducible objects of this decomposition theory. In this talk, we present a categorical framework for dynamical systems that significantly broadens the scope of our original approach. This generalization extends the decomposition theory to a wider class of systems, providing deeper insight into the structure-dynamics relationship and offering powerful new tools for analyzing complex biological networks.

Xingfu Zou

University of Western Ontario

"Infection forces mediated by behaviour changes with demonstration by a DDE model"

In this talk, we will revisit the notion of infection force from a new angle which can offer a new perspective to motivate and justify some infection force functions. Our approach not only can explain many existing infection force functions in the literature, it can also motivate new forms of infection force functions, particularly infection forces depending on disease surveillance of the past. As a demonstration, we propose an SIRS model with delay. We comprehensively investigate the disease dynamics represented by this model, particularly focusing on the local bifurcation caused by the delay and another parameter that reflects the weight of the past epidemics in the infection force. We confirm Hopf bifurcations both theoretically and numerically. The results show that depending on how recent the disease surveillance data are, their assigned weight may have a different impact on disease control measures.

Daniel B. Reeves

Fred Hutchinson Cancer Center

"Modeling HIV reservoir ecology and selection through the lens of CD4+ T cell kinetics"

The latent reservoir of HIV persists for decades in people living with HIV (PWH) on antiretroviral therapy (ART). To determine if persistence arises simply from natural behaviors of CD4+ T cells harboring HIV proviruses, we use ecological models to contrast the clonal dynamics of HIV vs memory CD4+ T cell sequences from the same PWH. We show HIV reservoirs are more clonal than general CD4+ T cells and that increasing reservoir clonality over time with decay of intact proviruses cannot be explained by CD4+ T cell kinetics alone. We develop a stochastic multitype branching process model that describes the dynamics of CD4+ T cells, some of which harbor HIV proviruses. We test nearly 1000 combinations of model mechanisms against a broad range of experimental observations, finding that weak selection against intact proviruses (s~0.06) is a parsimonious explanation for all data. These results help to understand the long-term dynamics of HIV reservoirs in PWH on ART and may inform immunotherapies for HIV cure.

Tianxu Wang

University of Alberta

"Cognitive Movement Strategies in a Food-Threat Dilemma"

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 or even individuals may prioritize different types of information. We investigate how various cognitive movement strategies affect species survival and extinction outcomes in simplified food–threat dilemmas. Specifically, we compare five commonly observed strategies using local, nonlocal maximum, global maximum, nonlocal aggregate, and global aggregate information. We prove the well-posedness of the model, where a general function of ODE variable appears in the taxis sensitivity function in PDE equation, and conduct stability and bifurcation analyses 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 highly depends on environmental context. The global maximum strategy enables survival with minimal foraging and threat avoidance effort in simple dilemmas, but in complex multimodal settings, the local strategy achieves the highest survival, while the global maximum performs worst.

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Annual Meeting for the Society for Mathematical Biology, 2025.