Dynamics and Asymptotic Profiles of Nonlocal Dispersal SIS Epidemic Models
报告专家：李万同(兰州大学)
报告时间： 8月9日（周二） 14：30-15：30
In this talk we consider a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model, where the spatial movement of individuals is described by a nonlocal (convolution) diffusion operator, the transmission rate and recovery rate are spatially heterogeneous, and the total population number is constant. We first define the basic reproduction number R_0 and discuss the existence, uniqueness and stability of steady states of the nonlocal dispersal SIS epidemic model in terms of R_0. Then we study the asymptotic profiles of the endemic steady states for large and small diffusion rates to illustrate the persistence or extinction of the infectious disease. The lack of regularity of the endemic steady state makes it more difficult to obtain the limit function of the sequence of endemic steady states. We also observe the concentration phenomenon which occurs when the diffusion rate of the infected individuals tends to zero. The obtained results indicate that the nonlocal movement of the susceptible or infectious individuals will enhance the persistence of the infectious disease. In particular, our analytical results suggest that the spatial heterogeneity tends to boost the spread of the infectious disease. This talk is based on joint works with Yan-Xia Feng (Lanzhou Univ.)、Shigui Ruan (Univ. Miami) and Fei-Ying Yang (Lanzhou Univ.)
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