MS01 - ECOP-05 Part 1 of 4

Celebrating 60 Years of Excellence: Honoring Yang Kuang’s Contributions to Mathematical Biology (Part 1)

Monday, July 14 at 10:20am

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Note: this minisymposia has multiple sessions. The other sessions are: Part-2 Part-3 and Part-4.

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.

Jianhong Wu

York University

"Population dynamics involving perceived risk-structured behavioural changes"

Behaviour changes and intervention takes place in response to perceived risks in the vector-host and pathogen-host interactions, leading to rich and complex population dynamics including multi-stability and oscillation birth and death. We will review a few models and analyses involving coupled systems of delay-differential equations and algebraic-integral equations.

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.

Rebecca Everett

Haverford College

"Stoichiometric ontogenetic development influences population dynamics: Stage-structured model under nutrient co-limitations"

Ecological processes depend on the flow and balance of essential elements such as carbon (C) and phosphorus (P), and changes in these elements can cause adverse effects to ecosystems. The theory of Ecological Stoichiometry offers a conceptual framework to investigate the impact of elemental imbalances on structured populations while simultaneously considering how ecological structures regulate nutrient cycling and ecosystem processes. While there have been significant advances in the development of stoichiometric food web models, these efforts often consider a homogeneous population and neglect stage-structure. The development of stage-structured population models has significantly contributed to understanding energy flow and population dynamics of ecological systems. However, stage structure models fail to consider food quality in addition to food quantity. We develop a stoichiometric stage-structure producer-grazer model that considers co-limitation of nutrients, and parameterize the model for an algae-Daphnia food chain. Our findings emphasize the impact of stoichiometric constraints on structured population dynamics. By incorporating both food quantity and quality into maturation rates, we demonstrate how stage-structured dynamics can influence outcomes in variable environments.

Eric Kostelich

Arizona State University

"Mathematical modeling for cancer dynamics and patient counseling"

In this talk, I will describe a mathematical approach to model the clinical evolution of recurrent glioblastoma. Given the poor prognosis, patient counseling and quality of life are key concerns. Because responses to treatment vary considerably, any modeling effort must account for the inevitable uncertainty in a given patient's clinical course. The goal of this project is to develop a system that can provide personalized estimates of the likely range of outcomes with a time horizon of two to three months. Our system can provide results in less than a minute on a laptop computer and so potentially could be packaged as an 'app' that can be used in a clinical setting for patient counseling. This talk will present the results of a preliminary retrospective modeling analysis of 137 magnetic resonance imaging studies of 46 unique patients who were previously treated at the Barrow Neurological Institute. This is joint work with Yang Kuang at ASU and Mark Preul of BNI.

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Annual Meeting for the Society for Mathematical Biology, 2025.