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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 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.
93A30Mathematical modelling of systems
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