Traveling Wave Solutions in a Nonlocal Dispersal SIR Epidemic Model with General Nonlinear Incidence.

In this paper, for a class of nonlocal dispersal SIR epidemic models with nonlinear incidence, we study the existence of traveling waves connecting the disease-free equilibrium with endemic equilibrium. We obtain that the existence of traveling waves depends on the minimal wave speed c ∗ and basic reproduction number R 0 . That is, if R 0 > 1 and c > c ∗ then the model has a traveling wave connecting the disease-free equilibrium with endemic equilibrium. Otherwise, if R 0 > 1 and 0 < c < c ∗ , then there does not exist the traveling wave connecting the disease-free equilibrium with endemic equilibrium. The numerical simulations verify the theoretical results. Our results improve and generalize some known results. [ABSTRACT FROM AUTHOR]