Traveling wave solutions in a discrete diffusive epidemic model with stage structure and nonlinear incidence rate

In order to understand the geographical spread of infectious diseases, classical epidemic models should consider spatial effects. Compared to the continuous diffusion version, the discrete diffusive version will be more realistic and meaningful. To our knowledge, there are not many studies on discrete diffusive epidemic models, therefore, this article investigates the existence, nonexistence, and asymptotic behavior of traveling wave solutions for a discrete diffusive epidemic model incorporating stage structure and a nonlinear incidence rate. Concretely, to begin with, we obtain the basic reproduction number. And then, we get that the critical wave speed determines the existence and nonexistence of traveling wave solutions. Meanwhile, by establishing an appropriate Lyapunov functional and applying Lebesgue dominated convergence theorem, we derive the boundary asymptotic behavior of traveling wave solutions. Ultimately, we employ these results to two examples (i.e. discrete diffusion stage epidemic models).