MS09 - MEPI-02

Modeling Complex Dynamics in Biological Processes: From Cellular Mechanics to Population-Level Dynamics (Part 2)

Friday, July 18 at 3:50pm

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

Folashade B. Agusto (University of Kansas), Chidozie Williams Chukwu

Description:

Summary: The study of complex biological systems requires a multi-faceted approach that integrates mathematical modeling and dynamical systems across scales. This mini symposium highlights innovative approaches that leverage dynamical systems and multi-scale models to address critical challenges in biology and public health. By spanning cellular, pathogen, and population-level dynamics, this mini-symposium aims to highlight the power of mathematical tools to uncover critical insights and inform strategies for addressing pressing challenges in health and disease. This mini symposium fosters interdisciplinary dialogue, emphasizing the transformative potential of mathematical biology in tackling real-world problems in public health an. Audience: This session will be of interest to mathematicians, ecologists, and biologists interested in modeling communicable and non-communicable diseases.

Chidozie Williams Chukwu

DePaul University, USA

"Dynamic Multi-country Modeling for Forecasting and Controlling Tube"

In this talk, we present a multi-country analysis of Tuberculosis (TB) epidemic model. We develop a deterministic TB model incorporating optimal control strategies and analyze its dynamics using mathematical tools. The model was calibrated using the new TB incidence data from India, Lesotho, Angola, and Indonesia. Numerical simulations are conducted to assess the impact of effective mask usage and case detection as intervention strategies. Our results project future trends of TB in the four countries studied. These insights are crucial for mitigating the spread of TB and addressing future challenges associated with potential TB outbreaks, particularly in the context of global public health crises.

Hewan Shemtaga, Selim Sukhtaiev, and Dr. Wenxian Shen

Auburn University, USA

"Logistic Keller-Segel chemotaxis models on compact graphs"

Chemotaxis phenomena governs the directed movement of micro-organisms in response to chemical stimuli. We investigate a pair of logistic type Keller–Segel systems of reaction-advection-diffusion equations modeling chemotaxis on networks. The distinction between the two systems is driven by the rate of diffusion of chemo-attractant. We prove the global existence of classical solution subject to Neumann-Kirchhoff vertex conditions without any conditions on chemotaxis sensitivity. In addition, we show that solutions with a non-negative and non-zero initial function converge to a globally stable constant solution for relatively small chemotaxis sensitivity. However, as chemotaxis sensitivity increase, we prove the constant solution loses stability and there exist other non-constant steady states bifurcating from the constant solution.

Ousmane Seydi

University Le Havre, France

"Growth Bounds and Threshold Dynamics in Periodic Structured Population Models"

Understanding when a population will grow, decline, or persist over time is a central question in mathematical biology. In this talk, we present a general method for identifying the conditions under which population growth occurs, even in models that incorporate age-structure, nonlocal interactions, or delays. Our approach applies to a broad class of mathematical systems, and we provide tools to compute critical threshold values—such as reproduction numbers—and to explain how these values determine the long-term behavior of the population. This framework draws on ideas from operator theory and dynamical systems to gain insight into biological processes that are periodic in time.

Daniel Cooney

University of Illinois Urbana-Champaign, USA

"Modeling Cross-Scale Evolutionary Dynamics"

Natural selection often operates simultaneously across multiple levels of biological organization, with evolutionary tensions often arising between traits or behaviors that are favored at different levels of selection. One common example of this tension arises in the evolution of altruism in group-structured populations, in which actions that are costly and result in an individual-level disadvantage while providing a collective benefit to the individual’s group. In this talk, we will explore a variety of PDE models that use evolutionary game theory to describe the evolution of altruism under competition occur both within and among groups, and we will discuss how different formulations of individual-level and group-level birth and death events can impact the long-time support for cooperation under these PDE models.

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Annual Meeting for the Society for Mathematical Biology, 2025.