Analysis of a vector-borne disease model with human and vectors immigration

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Résumé

We study the stability analysis of a vector-borne disease model. A wind-borne long- distance immigration of vectors and human immigration are considered. We assume a nonlinear incidence function including mass action and saturating incidence as special cases. There is no disease-free equilibrium and therefore no basic reproduction number. The only equilibrium is an endemic equilibrium. By the Lyapunov method, we show that this endemic equilibrium is globally asymptotically stable. We established that when the fraction of infective human and vectors immigrants approaches a small value, there is a threshold for which the disease can be reduced in the community.

Mots-clés

Vector-borne diseases, Immigration, Global stability, Lyapunov function