讲座题目： Dynamics of a Reaction-Diffusion SIS Epidemic Model

主办单位：数理学院/三峡数学研究中心

报告专家：郭志明

报告时间：2025年11月1日 (周六)  14:00

腾讯会议：876-763-047

专家简介：郭志明，广州大学数学与信息科学学院二级教授、博士生导师。2001年博士毕业于中山大学，2009年在加拿大西安大略大学访问一年。多年来一直从事离散系统、泛函微分方程及生物数学模型的理论与应用研究，在JDE, J. London Math. Soc., SIAP, JDDE, JMB和《中国科学》等国际国内重要刊物上发表论文90多篇，其中SCI收录70多篇。先后主持国家自然科学基金面上项目5项、参加国家自然科学基金重点项目1项。获得2021年度广东省自然科学奖一等奖。

报告摘要：Many infectious diseases show distinct spatiotemporal decoupling: evolutionary processes precede dispersal, and epidemiological data are usually collected at fixed time intervals, so discrete-time diffusion epidemic models may offer a more realistic representation of epidemiological dynamics compared to their continuous-time counterparts. In this talk, we introduce a modeling framework for discrete-time reaction-diffusion epidemic systems in heterogeneous environments. The variational characterization of the basic reproduction numberis established and its monotonicity with respect to the diffusion rate is discussed. The existence, uniqueness and stability of steady states in terms of are studied. Finally, the asymptotic behaviors of the unique endemic equilibrium are analyzed when the diffusion rate of either the susceptible or infected individuals tends to infinity or zero. Our results reveal that the optimal strategy of eliminating the disease at least at low-risk sites is to restrict the diffusion of infected individuals.