Modeling And Analysis For A Vector-borne Disease With Acute And Chronic Stage

The vector-bome disease transmission model with acute and chronic stage is formulated and analyzed. It is shown that the global dynamical behavior of this model is completed determined by Ro, that is, the disease free equilibrium is global asymptotical stableifRo<1, in this case.the disease will die out; The endemic equilibrium is global asymptotical stable if Ro>1, in this case, the disease will persist in population. The control model of the vector-borne disease is also formulated by introducing a control variable. The existence and explicit expression of the optimal control is given and proven, respectively. Numerical simulators are given to support the theoretical results obtained in this paper.