Dr. Zhisheng Shuai (UCF School of Data, Mathematical, and Statistical Sciences) will speak on "The Mathematics of Spatial Ecology and Epidemiology: A Perspective from Matrix and Graph Theory" at this week's seminar.
Abstract: Understanding how spatial and temporal heterogeneity influences population and disease dynamics is a central challenge in ecology and epidemiology. In this talk, we explore mathematical approaches that connect matrix theory, graph theory, and differential equations to model and analyze these complex systems. In particular, we demonstrate how generalized inverses and related linear algebra and graph theory tools can quantify variability in population persistence, growth rates, and disease invasibility across heterogeneous habitats. By integrating these techniques with differential equation models, we examine the effects of habitat structure, resource distribution, and migration on population stability and disease spread. The talk highlights how mathematical frameworks provide novel insights into ecological resilience, conservation strategies, and infectious disease management, illustrating to a general audience the interplay between mathematical theory and real-world biological systems.
Short Bio: Dr. Zhisheng Shuai is a Professor of Mathematics in the School of Data, Mathematical, and Statistical Sciences at the University of Central Florida (UCF). Prior to joining UCF in 2012, he earned his Bachelor of Science in Mathematics and Master’s Degree in Applied Mathematics at the Northeast Normal University, China. He then earned his PhD in Applied Mathematics from the University of Alberta, before completing an NSERC Postdoctoral Fellowship at the University of Victoria, supported by the prestigious Natural Sciences and Engineering Research Council of Canada. Dr. Shuai’s research focuses on mathematical ecology and epidemiology, differential equations, and dynamical systems. His current research investigates how various mathematical modeling approaches can be used to study the complex dynamics of infectious diseases. Beyond his research, Dr. Shuai has played a significant role in UCF’s Mathematical Modeling curriculum and has led efforts to recruit and train UCF teams, resulting in impressive ranking in various math modeling competitions. He has been honored with the UCF Teaching Incentive Program (TIP) award for his outstanding teaching. Dr. Shuai also serves as a reviewer for several research journals, including the Society for Industrial and Applied Mathematics (SIAM) Journals on Applied Mathematics, Differential Equations and Dynamical Systems, among many others.
Read More