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Traveling waves for a four‐compartment lattice epidemic system with exposed class and standard incidence

This paper is considering the problem of traveling wave solutions (TWS) for a susceptible‐exposed‐infectious‐recovered (SEIR) epidemic model with discrete diffusion. The threshold condition for the existence and nonexistence of TWS is obtained. More specifically, such kind of solutions are governed by the threshold number ℜ0. We can find a critical wave speed c∗ if ℜ0 > 1, by employing the Schauder's fixed point theorem, limiting argument and two‐sided Laplace transform, we confirm that there exists TWS for c > c∗, while there exists no TWS for c < c∗. We also obtain the nonexistence of TWS for ℜ0   ≤   1. At last, we give some biological explanations from the epidemiological perspective.