| Abstract: |
| In this talk we consider a nonlocal dispersal SIS epidemic model, where the spatial movement of individuals is described by a nonlocal diffusion operator, the transmission rate and recovery rate are spatially heterogeneous. 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. 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. |
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