Travelling wave solutions for a reaction-diffusion influenza model with general incidence and treatment

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.