MS08 - ECOP-07

Exploring Heterogeneity in Mathematical Models: Methods, Applications, and Insights (Part 3)

Friday, July 18 at 10:20am

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

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.

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Annual Meeting for the Society for Mathematical Biology, 2025.