Wave propagation for a discrete diffusive mosquito-borne epidemic model. (English) Zbl 1535.35031
Summary: 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 \(c^\ast\). More precisely, when \(R_0 > 1\) and \(c \geq c^\ast\), 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 \(0 < c < c^\ast\) or \(R_0 \leq 1\), the system has no nontrivial traveling wave solution by using a contradictory approach and two-sided Laplace transforms.
MSC:
| 35C07 | Traveling wave solutions |
| 35K57 | Reaction-diffusion equations |
| 39A12 | Discrete version of topics in analysis |
| 92D30 | Epidemiology |
Keywords:
mosquito-borne epidemic model; discrete diffusion; traveling wave solutions; existence; nonexistenceReferences:
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