报告题目：Asymptotic Profiles of Endemic Equilibria in an SIS Reaction-Diffusion Model with a Protected Zone

报告人：姜智北博士，长沙理工大学

报告时间：2026年9月30日（周三）14:30-17:30

报告地点：20-200

报告摘要：A steady-state SIS reaction-diffusion system is considered on a bounded domain partitioned into an infectious zone and a protected zone where the transmission rate vanishes. The system admits a unique endemic equilibrium whenever the basic reproduction number R0>1. Three asymptotic regimes are analyzed. As the transmission rate in the infectious zone tends to infinity, the susceptible density vanishes and the infected density approaches a positive constant in the infectious zone, while the infected density in the protected zone converges to the solution of a mixed boundary value problem. As the diffusion rate of susceptible individuals tends to zero, the infected population vanishes uniformly on the entire domain, yet the limiting susceptible profile is not the disease-free equilibrium. In one dimension, as the diffusion rate of infected individuals tends to zero, the susceptible density converges uniformly to the minimum of the risk function, the infected population vanishes uniformly on the protected zone, and the infected mass concentrates at the locations of highest risk in the infectious zone. Finally, R0 is shown to decrease strictly with the size of the protected zone.

报告人简介：姜智北，长沙理工大学数学与统计学院教师，主要从事传染病反应扩散模型研究，研究成果发表于Journal of Differential Equations、Journal of Mathematical Analysis and Applications、Discrete and Continuous Dynamical Systems Series B等期刊。

邀请人：无穷维动力系统和偏微分方程研究所