MS08 - ECOP-07 Part 2 of 3

Exploring Heterogeneity in Mathematical Models: Methods, Applications, and Insights (Part 2)

Friday, July 18 at 10:20am

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

Zhisheng Shuai (University of Central Florida), Junping Shi, College of William & Mary; Yixiang Wu, Middle Tennessee State University

Description:

This minisymposium will focus on the mathematical modeling of heterogeneity across various biological systems. Heterogeneity often plays a critical role in shaping the dynamics and outcomes of biological processes. The session aims to: (i) Showcase advances in modeling techniques that capture heterogeneity; (ii) Explore the impact of heterogeneity on predictions and control strategies; (iii) Highlight applications spanning population dynamics, epidemiology, ecology and evolution; (iv) Encourage discussions on the integration of data-driven and theoretical approaches to address heterogeneity. We have confirmed 10 speakers, with 2 more awaiting confirmation (one pending administrative approval at the CDC). Among the confirmed speakers, half are female, and over half are junior researchers, including 1 PhD student and 2 postdocs. Please note that we are going to submit another proposal for the total of 12 speakers.

Yuanwei Qi

University of Central Florida

"Mathematical Analysis of a Cancer Invasion Model"

In this talk I shall present some recent results on Global Existence, Stability of various equilibrium points as well as existence of traveling wave to a well established reaction-diffusion system modeling cancer invasion. This is a joint work with Xinfu Chen of University of Pittsburgh, Xueyan Tao and Shulin Zhou of Peking University.

Chunhua Shan

University of Toledo

"Transmission dynamics and bifurcations of a diffusive epidemic model with a nonlinear recovery rate"

In this talk we study the disease transmission dynamics of a diffusive epidemic model with a nonlinear recovery rate. The Hopf bifurcation and Bogdanov-Taken bifurcation are first considered for the corresponding ODE model. Then we analyze the Turing instability and the Turing-Hopf bifurcation. Numerical simulations and biological interpretation are also provided.

Yixiang Wu

Middle Tennessee State University

"Analysis of a parabolic-hyperbolic hybrid population model: an integrated semigroup approach"

We consider the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison principle, and demonstrate the asymptotic smoothness of the solution semiflow. Through the spectral analysis of the linearized system, we derive and characterize the net reproductive rate $mathcal{R}_{0}$. Furthermore, an explicit relationship between $mathcal{R}_{0}$ and the principal eigenvalue of the linearized system is analyzed. Under appropriate monotonicity assumptions, we show that $mathcal{R}_{0}$ serves as a threshold parameter that completely determines the global stability of the system. This is a joint work with Qihua Huang and Mingling Wang.

Poroshat Yazdanbakhsh

Rollins College

"A Novel Approach to Understanding Disease Spread and Population Persistence in Heterogenous Environments"

How do infectious diseases or species populations evolve in heterogeneous environments? This has been one of the most sought-after questions in the field of mathematical biology. In this talk, we aim to address this question by introducing a new measure called the network heterogeneity index, denoted by H. We offer a fresh perspective to better understand how diseases spread and populations persist in heterogeneous environments. Our analysis shows that how H is influenced by several key factors, including the structure of such networks, regional disease or population dynamics, and the movements between regions. To highlight the importance of H, we conclude our talk by exploring its applications in epidemiology and ecology across various heterogeneous settings.

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Annual Meeting for the Society for Mathematical Biology, 2025.