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 \( I_{h0}^c = \frac{b_h}{\mu_h} \) for the infective human population level \( I_{h0} \) at which the health care system reaches its capacity. We derive that when \( I_{h0} \geq I_{h0}^c \), the dynamics of the model is completely determined by the basic reproduction number \( R_0 \). When \( I_{h0} < I_{h0}^c \), the model exhibits multiple endemic equilibria.