The Dynamical Analysis Of Vector-born Epidemic Models With Control Strategies

In recent years, the research on dynamic behaviour of vector-borne disease model has been widely concerned by a number of scholars, Our paper has launched a detailed research about the dynamical behaviors of two vector-borne epidemic models and dis-cussed the effects of impulsive control and prevention on disease. Its main contents can be summarized as follows:1. In the first part, we established Rift Valley Fever model with impulsive vaccina-tion. By using direct analysis method, qualitative analysis theory, comparison principe, integral and differential inequalities, and some of analytical skills, theoretical condition-s about persistence and extinction of RVFV are obtained under impulsive control, at last, numerical simulation is given to verify the correctness of the theoretical results and feasibility of the impulsive control measure.2. In the second part, we established a class dengue fever model with impulsive control strategy and standard incidence. Accurate expression of the basic reproduction number 1Z was established, that is, whenR< 1, the disease-free periodic solution is global asymptotically stable, to the contrary, when R> 1, the disease is uniform persistence.3. In the third part, we established dengue fever model with impulsive culling vector and saturated incidence, which spreads between human and mosquitoes and established sufficient condition about the stability of the disease and the uniform persistence of the disease and illustrated existence condition on backward bifurcation of model. We have discussed the effects of impulsive control and prevention on disease. Numerical simulation is given to verify the correctness of the theoretical results and feasibility of the control measure, which illustrates the dengue fever is controlled and even eliminated by adjusting the strength of the control measures.