A Kind Of Sis Epidemic Model With Stage Qualitative Analysis

The existence of epidemic has serious impact on human health. We established epidemic mathematical models of epidemics, analyzing those models qualitatively and quantitatively and predicting the trends of the epidemics. The article consists of three chapters.In chapter one, we mainly introduced the background of epidemics, mathematical models of epidemics and some pretest knowledge, such as important concepts theories which are used in our paper.In chapter two, we established one type of SIS model with a stage structure. First, we studied the existence of the equilibrium and the sufficient conditions of locally asymptotically stable of the equilibria is studied by the Routh-Hurwitz criterion. By constructing appropriate Dulac function the global stability of the equilibria is investigated. Finally, numerical simulation results are given to support the theoretical results.In chapter three, we mainly derived one type of SIS model with Logistic growth. The basic reproduction number (R0) for determining whether a disease is extinct or not is found. It is proved that the disease-free equilibrium is unstable and the sufficient conditions of locally asymptotically stable of the other two equilibriums. Furthermore, a numerical simulation results are given to support the theoretical results.