Study On The Stability Of Two Kinds Of Infectious Disease Dynamics Model

The development process of disease is studied by infectious disease dynamics, using the dynamical method. In this paper, we have studied the stability of two kinds of infectious disease model(HIV model and SIR model), the main content as follows:Firstly, we described the development history and the recurrent studies of infectious disease model, introduced some basic concepts, several corresponding results and the main result of our work.Secondly, we premeditated the dynamic behavior and the control measure about the spread of HIV, focusing on the people who is injecting drug users(IDUs), female sex workers(FSWs) and clients of female sex workers(CFSWs). We constructed a dynamics model Based on it and obtained the basic reproduction number R0. We have proved the globally asymptotic stability of the disease-free equilibrium E0 when R0< 1. The boundary equilibria E1 and E2are globally asymptotically stable in certain conditions. If R0> 1, we can get the globally asymptotic stability of the endemic equilibrium E?. We compared the actual data with the simulation results and predicted the spread tend of HIV through numerical simulation. In addition, we also discussed the prevention and control measures for HIV.Finally, we investigated the global stability of an SIR model with di?erential susceptibility and infectivity. The basic reproduction number R0 and the existence condition of epidemic equilibrium are obtained. the disease-free equilibrium is globally asymptotically stable when R0< 1; If R0> 1, the endemic equilibriums of the model is exist and unique,which is globally asymptotically stable. Then a series of numerical simulations are presented to illustrate our mathematical ?ndings.