ABSTRACT.

In this paper, we analyze a vector-host epidemic model with a piecewise smooth treatment rate. The use of piecewise-smooth treatment depicts the limited medical resource situation in the community. The treatment increases linearly with infective population until the treatment capacity is reached, after which constant treatment(i.e maximum treatment) is applied. The analysis indicates that there exists a critical value Ich0 = bhμh for the infective human population level Ih0 at which the health care system reaches its capacity. We derive that when Ih0 → Ich0, the namics of the model is completely determined by the basic reproduction number R0. When Ih0 < Ich0, the model exhibits multiple endemic equilibria.