The global stability for a vector-host epidemicModel

In this paper, a five-dimensional vector-host epidemic model with temporary immunity is studied. Applying autonomous convergence theorem, the basic reproduction number is proved to be a sharp threshold which completely determines the global dynamics and the outcome of the disease. If the reproduction number is less than or equal to one, the disease-free equilibrium is globally asymptotically stable in the feasible region and the disease always dies out. If the reproduction number is greater than one, a unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region and the disease will persist at the endemic equilibrium if it is initially present.