报告题目：Asymptotic profiles of the steady states for an SIS epidemic patch model with asymmetric connectivity matrix
报 告 人：吴毅湘 博士，美国中田纳西州立大学（Middle Tennessee State University ）
时 间：2019年元月7日（周二）下午4:00-5:00
地 点：数学院425
摘要: The dynamics of an SIS epidemic patch model with asymmetric connectivity matrix is analyzed. It is shown that the basic reproduction number $R_0$ is strictly decreasing with respect to the dispersal rate of the infected individuals, and the model has a unique endemic equilibrium if $R_0>1$. The asymptotic profiles of the endemic equilibrium for small dispersal rates are characterized. In particular, it is shown that the endemic equilibrium converges to a limiting disease-free equilibrium as the dispersal rate of susceptible individuals tends to zero, and the limiting disease-free equilibrium has a positive number of susceptible individuals on each low-risk patch. Moreover a sufficient and necessary condition is found to guarantee that the limiting disease-free equilibrium has no positive number of susceptible individuals on each high-risk patch. Our results extend earlier results for symmetric connectivity matrix, and we also partially solve an open problem by Allen et. al
