Abstract:

This paper is concerned with a nonlocal dispersal SIR model. We first prove the existence of critical traveling wave for this model when $ {\cal R}_0>1 $, $ c=c^* $. Finally, the nonexistence of traveling wave solution for this model is established when $ {\cal R}_0<1 $. Our results improve some known results.

Key words: Nonlocal dispersal, SIR model, Critical wave speed, Traveling wave