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.

Yun Kang

Arizona State University

"Recognizing and Honoring Yang Kuang’s Contributions to Mathematical Biology"

This presentation is dedicated to celebrating the extraordinary career of Professor Yang Kuang, whose pioneering contributions have left a lasting impact on the field of mathematical biology. Professor Kuang's research, spanning ecological stoichiometry, delay differential equations, partial differential equations, and data-driven modeling, has shaped critical directions in both theoretical and applied biosciences. Beyond his influential scientific achievements, Dr. Kuang is widely recognized for his collaborative spirit and unwavering dedication to mentoring. Over the course of his career, he has guided 29 Ph.D. students and mentored numerous postdoctoral fellows, master’s students, and undergraduates, many of whom have gone on to make significant contributions to academia, industry, and government. In this talk, we will share personal reflections, quotes, and experiences collected from Dr. Kuang’s former students, postdoctoral scholars, and collaborators. Through their stories, we aim to highlight not only his profound academic influence but also his remarkable legacy as a mentor, role model, and community builder. This celebration honors both the depth of Dr. Kuang’s scholarship and the far-reaching impact he has had in shaping the next generation of mathematical biologists.

Jiaxu Li

University of Louisville

"A class of delay differential equation system and its applications"

Time delays are inherent in biological systems, appearing in processes such as physiological feedback loops, drug delivery, therapeutic interventions, and the cyclical harvesting of fish and restocking of fry in aquaculture operations. Numerous delay differential equation (DDE) models have been developed to study these systems. However, many of these models fall short in fully capturing the dynamics and delayed effects of interventions that are administered at discrete time intervals and gradually absorbed by the system. Despite advances in artificial intelligence (AI), modeling complex biological systems—such as glucose-insulin regulation—remains a significant challenge. Personalized algorithms often face limitations due to insufficient training data, while delay-induced uncertainties (DIUs) can lead to chaotic behavior, further complicating the development of effective control strategies. A deep understanding of these dynamic behaviors and their implications is essential for designing accurate and robust interventions. In this talk, we present a novel modeling framework that accounts for both the intrinsic time delays in biological systems and the delayed effects of time-distributed interventions, with the goal of improving system effectiveness and sustainability. Applications include artificial pancreas systems for single-hormone (insulin) and dual-hormone (insulin and glucagon) delivery, tumor treatment strategies, and population dynamics models incorporating optimized intermittent restocking and harvesting to promote ecological balance.

Bingtuan Li

University of Louisville

"Forced Traveling Waves in a Reaction-Diffusion Equation with a Strong Allee Effect and Shifting Habitat"

Renewed interest in spatial ecology has emerged, largely due to the threats posed by global change. Shifts in habitat suitability for many species have already occurred and are expected to continue, profoundly affecting invasion dynamics. In this study, we consider a reaction-diffusion equation modeling the growth of a population subject to a strong Allee effect within a bounded habitat that shifts at a constant speed c. We demonstrate that the existence of forced positive traveling waves depends on the habitat size L and on c∗, the wave speed for the corresponding reaction-diffusion equation defined over an unbounded spatial domain with the same growth function. Specifically, we show that when c∗>c>0, there exists a positive threshold L∗(c) such that two positive traveling waves exist if L>L∗(c), while no positive traveling wave exists if Lc∗, then for any L>0, no positive traveling wave exists. These theoretical results are complemented by numerical simulations that explore the equation’s dynamics in greater detail.

Clay Prater

University of Arkansas

"I get by with a little help from my friends: Adventures in stoichiometric modeling of a mathematically challenged empirical ecologist"

Organisms interact with their environments through the exchange of elements and energy. However, predicting the effects of insufficient supplies of these resources on organismal growth has been a longstanding challenge. To this end, we developed a conceptual framework, the growth efficiency hypothesis, which posits strong mechanistic relationships among organismal resource contents, use efficiencies, and growth rate. We tested this hypothesis by exposing consumers to multiple forms of resource limitation, which resulted in unique differences in their resource composition. These differences reflected physiological changes serving to optimize resource use efficiencies and were used to generate accurate predictions of consumer growth rate. Our findings demonstrate the growth efficiency hypothesis to be a powerful framework for understanding the multivariate nature of resource limitation.

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Annual Meeting for the Society for Mathematical Biology, 2025.