MS05 - MEPI-08

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

Wednesday, July 16 at 10:20am

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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.

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.

Gregoire Ranson

York University

"Qualitative impact of political and economic decisions on PrEP users under HIV epidemic control"

In this work, we explore the dynamics of a hybrid differential–difference system with delay describing an HIV SI-model with protected compartment (PrEP) described by an age-structured equation and nonmonotonic recruitment rate. The limited protection duration offered induces a delay in the system. First, we study the existence of equilibria. Under our assumption, we show that the system exhibits several steady states without infection, which challenges the study. After a local stability analysis of each equilibrium, we study the existence of a Hopf bifurcation around the endemic equilibrium. Our results show that the delay may destabilize the endemic steady state and lead to the existence of recurrent periodic epidemic waves. Each situation is illustrated by numerical simulations.

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Annual Meeting for the Society for Mathematical Biology, 2025.