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 of the corresponding kinetic system and the critical wave speed c ∗ . More precisely, when R 0 > 1 and c ≥ c ∗ , 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 ∗ or R 0 ≤ 1 , the system has no nontrivial traveling wave solution by using a contradictory approach and two-sided Laplace transforms. [ABSTRACT FROM AUTHOR]