In this paper, a reaction-diffusion epidemic model with general nonlinear incidence and treatment is proposed. The basic reproduction number R0 and the critical wave speed c∗ are defined, and the existence and nonexistence of travelling wave solutions satisfying certain boundary conditions is investigated by some fixed point theorems, two-sided Laplace transform method and Stable Manifold Theorem. Specifically, when R0>1 and c>c∗, then the existence of the travelling wave solutions is established. When R0>1 and 00 the non-existence of travelling wave solutions also is established. Finally, we present the numerical simulations and investigate the effect of the critical wave speed on disease propagation.
Duan et al. (Fri,) studied this question.