题目：Multiplicity and asymptotic profiles of endemic equilibria of a cross-diffusive epidemic model

主讲人：薛书文 博士

时间：2025年6月24日（星期二）10:00

地点：理学院315会议室

主办单位：理学院

主讲人简介：

薛书文，美国北伊利诺伊大学数学科学系助理教授。2021年博士毕业于美国奥本大学，博士导师为沈文仙教授。2021年至2022年在加拿大纽芬兰纪念大学数学与统计系任AARMS博士后研究员。博士后导师为赵晓强教授。研究方向主要为微分方程、动力系统和生物数学。在Journal of Mathematical Biology, Journal of Differential Equations, Journal of Dynamics and Differential Equations and Discrete and Continuous Dynamical Systems-Series A等期刊发表论文多篇。

摘要：

Spatial heterogeneities in the environment and the movements of individuals play crucial roles in the spread of infectious diseases. In this talk, we focus on a cross-diffusive epidemic model that incorporates the repulsive movement of susceptible population away from infected population. First, we will introduce the model. Then, we show that the basic reproduction number alone cannot determine the existence of endemic equilibria (EEs) and the model may have multiple EEs when the repulsive movement rate is large. Next, we analyze the bifurcation curves of EEs. Specifically, we show that a large repulsive movement rate tends to induce backward bifurcation curves. This highlights the complex dynamics of the system under strong repulsive interactions. Finally, we investigate the asymptotic profiles of EEs as the repulsive movement rate is large or the random movement rates are small. Our findings indicate that a large tendency of susceptible people to avoid infected people can eliminate the disease if and only if the total population is below a critical number.