Abstract
In this paper, we investigate the existence and nonexistence of traveling wave solutions in a nonlocal dispersal epidemic model with spatio-temporal delay. It is shown that this model admits a nontrivial positive traveling wave solution when the basic reproduction number $ R_0>1 $ and the wave speed $ c\geq c^* $ ($ c^* $ is the critical speed) and this model has no traveling wave solutions when $ R_0\leq1 $ or $ c<c^* $. This indicates that $ c^* $ is the minimal wave speed.
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