Wave Propagation for a Discrete Diffusive Mosquito-Borne Epidemic Model

This paper is concerned with the existence and nonexistence of traveling wave solutions for a discrete diffusive mosquito-borne epidemic model with general incidence rate and constant recruitment. It is observed that whether the traveling wave solutions exist or not depend on the so-called basic reproduction ratio \(R_0\) $R_0$ of the corresponding kinetic system and the critical wave speed \(c^*\) $c^{\ast }$ . More precisely, when \( R_0 >1\) $R_0>1$ and \(c\ge c^*\) $c\ge c^{\ast }$ , the system admits a nontrivial traveling wave solution by constructing an invariant cone in a bounded domain with initial functions being defined on, and employing the method of upper and lower solution, Schauder’s fixed point theorem and a limiting approach. Moreover, the asymptotic behavior of traveling wave solutions at positive infinity is obtained by constructing a suitable Lyapunov functional. When \(0<c<c^*\) $0<c<c^{\ast }$ or \( R_0 \le 1\) $R_0\le 1$ , the system has no nontrivial traveling wave solution by using a contradictory approach and two-sided Laplace transforms.