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Global stability of an epidemic model for vector-borne disease. (English) Zbl 1197.93059
Summary: This paper considers an epidemic model of a vector-borne disease which has the vectormediated transmission only. The incidence term is of the bilinear mass-action form. It is shown that the global dynamics is completely determined by the basic reproduction number ${R}_{0}$. If ${R}_{0}\le 1$, the diseasefree equilibrium is globally stable and the disease dies out. If ${R}_{0}>1$, a unique endemic equilibrium is globally stable in the interior of the feasible region and the disease persists at the endemic equilibrium. Numerical simulations are presented to illustrate the results.
##### MSC:
 93A30 Mathematical modelling of systems
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