Dynamical Study Of Two Classes Of Nonlinear Epidemic Models

In this paper,we mainly study the dynamics of two classes of infectious disease systems.The article includes three chapters.The preface is in chapter 1,we introduce the research background of this article.the main task and some important preliminaries.In Chapter 2,used with general nonlinear incidence Sg(?),we established with nonlinear incidence rate and cure rate to HIV/AIDS epidemic model.In this model,the change of behavior habit of patients with HIV after treatment was considered.First.of all,The regeneration matrix is used to obtain the basic regeneration number of the model and the existence of the equilibrium point of the model.Then,we study global stability of the disease-free equilibrium and the unique endemic equilibrium by using the qualitative theory of ordinary differential equation.In the end,numerical simulations are carried out to verify the theoretical results in this chapterIn Chapter 3,the fractional order derivative is introduced to set up a class of SIR epi-demic model with Logistic growth,saturated cure rate in time delay,make the system more general.Firstly,the existence of the system equilibrium is discussed.Secondly,we showed lo-cally asymptotic stability of the disease-free equilibrium point of the model by using the method of characteristic value,and the local asymptotic stability conditions of the positive equilibrium point are obtained by using the stability theory of fractional-order differential equation.Fi-nally,by constructing Lyapunov function we proved the disease-free equilibrium and the unique endemic equilibrium of the model are uniformly asymptotic stability.