MS09 - ECOP-05

Celebrating 60 Years of Excellence: Honoring Yang Kuang’s Contributions to Mathematical Biology (Part 4)

Friday, July 18 at 4:00pm

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Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-2, and Part-3.

Tin Phan (Los Alamos National Laboratory), Yun Kang (Arizona State University); Tracy Stepien (University of Florida)

Description:

This session is organized to honor Professor Yang Kuang for his pioneering contributions to mathematical biology, his spirit of collaboration, and his dedication to mentoring 28 PhD students, as well as numerous postdoctoral, master's, and undergraduate researchers. Invited speakers will present cutting-edge research inspired by Dr. Kuang’s foundational work, spanning ecological stoichiometry, delay and partial differential equations, and data-driven modeling in biology. Together, we highlight Dr. Kuang’s achievements and the profound influence his work has on guiding the next generation of researchers in mathematical biology.

Bruce Pell

Lawrence Technological University

"Stability Switching Induced by Cross-Immunity in a Two-Strain Virus Competition Model with Wastewater Data Validation"

We study a two-strain virus competition model incorporating temporary immunity through a discrete delay. After reducing and analyzing the system, we identify stability switching phenomena at the strain-1-only equilibrium, including the occurrence of Hopf bifurcations. A detailed characterization of the stability dynamics at this equilibrium is provided. We further validate the model using wastewater surveillance data and apply it to investigate the viral shedding behavior of recovered individuals.

Tianxu Wang

University of Alberta

"Derivations of Animal Movement Models with Explicit Memory"

Highly evolved animals continuously update their knowledge of social factors, refining movement decisions based on both historical and real-time observations. Despite its significance, research on the underlying mechanisms remains limited. In this study, we explore how the use of collective memory shapes different mathematical models across various ecological dispersal scenarios. Specifically, we investigate three memory-based dispersal scenarios: gradient-based movement, where individuals respond to environmental gradients; environment matching, which promotes uniform distribution within a population; and location-based movement, where decisions rely solely on local suitability. These scenarios correspond to diffusion advection, Fickian diffusion, and Fokker-Planck diffusion models, respectively. We focus on the derivation of these memory-based movement models using three approaches: spatial and temporal discretization, patch models in continuous time, and discrete-velocity jump process. These derivations highlight how different ways of using memory lead to distinct mathematical models. Numerical simulations reveal that the three dispersal scenarios exhibit distinct behaviors under memory-induced repulsive and attractive conditions. The diffusion advection and Fokker-Planck models display wiggle patterns and aggregation phenomena, while simulations of the Fickian diffusion model consistently stabilize to uniform constant states.

Lifeng Han

Tulane University

"A Simplified Model of Cancer Vaccine with Two Different Tumor-Immune Functional Responses"

This talk is dedicated to celebrating Dr. Yang Kuang’s profound influence on the field of mathematical biology and his pivotal role in shaping my own journey into mathematical oncology. In this work, I explore a simplified model of cancer vaccine incorporating two commonly used functional forms for immune-mediated tumor cell killing: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). Through analytical techniques, we uncover how each functional response yields distinct biological insights. Notably, we find that under the LPR formulation, tumor elimination depends on the initial condition—offering mathematical support for the clinical practice of using cancer vaccines as an adjuvant therapy.

Tin Phan

Los Alamos National Laboratory

"The development and validation of a modeling framework for HIV treatment"

Most people living with HIV-1 experience rapid viral rebound once antiretroviral therapy is interrupted; however, a small fraction remain in viral remission for extended periods. Understanding the factors that determine whether viral rebound is likely after treatment interruption can inform the development of optimal treatment regimens and therapeutic interventions aimed at achieving a functional cure for HIV-1. Building upon the theoretical framework proposed by Conway and Perelson, we iteratively formulated and examined hundreds of dynamic models of virus–immune interactions to identify those that both recapitulate viral dynamics across all studies and generate predictions consistent with clinical observations. We evaluated these models using extensive longitudinal viral-load and immunological data from multiple clinical trials. The best-performing models accurately capture the heterogeneity of viral dynamics from the acute phase through rebound. Our results robustly demonstrate that the expansion capacity of effector cells is a key determinant of viral control.

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Annual Meeting for the Society for Mathematical Biology, 2025.