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This paper studies an epidemic model with nonlocal dispersals. We focus onthe influences of initial data and nonlocal dispersals on its spatialpropagation. Here the initial data stand for the spatial concentrations ofinfectious agent and infectious human population when the epidemic breaks outand the nonlocal dispersals mean their diffusion strategies. Two types ofinitial data decaying to zero exponentially or faster are considered. For thefirst type, we show that the spreading speeds are two constants whose signschange with the number of elements in some set. Moreover, we find aninteresting phenomenon: the asymmetry of nonlocal dispersals can influence thepropagating directions of solutions and the stability of steady states. For thesecond type, we show that the spreading speed is decreasing with respect to theexponentially decaying rate of initial data, and further, its minimum valuecoincides with the spreading speed for the first type. In addition, we givesome results about the nonexistence of traveling wave solutions and themonotone property of solutions. Finally, some applications are presented toillustrate the theoretical results.

Spatial Propagation in an Epidemic Model with Nonlocal Diffusion: the Influences of Initial Data and Dispersals