Analysis Of Stability For Some Classes Of Epidemic Model

There are still many infectious diseases that endanger human health,therefore it is of practical significance and realistic value to study the dynamics of the model of infectious diseases.Recently,more and more scholars use differential equations to investigate the infectious diseases.This paper,by using differential inequalities and comparison principle which are quite different from Lyapunov function,has studied the bilinear incidence and standard incidence of one group dynamics properties of SIR model,and promote these methods to two groups SIR model.In Chapter 1,we mainly introduce the background and development situation of the subject,and give some theoretical tools and preliminaries.In Chapter 2,an SIR epidemic model with bilinear incidence is considered.We get the basic reproduction number and the stability of the disease-free equilibrium is analyzed.The local stability of endemic equilibrium is obtained and with the help of the differential inequalities and the comparison principle,the global stability of endemic equilibrium is obtained under certain restriction conditions.At the same time,some numerical simulations are given to verify our conclusions.In Chapter 3,an SIR epidemic model with standard incidence is studied.We get the basic reproduction number and the stability of the disease-free equilibrium is analyzed.The local stability of endemic equilibrium is analyzed and with the help of the differential inequalities and the comparison principle,the global stability of the endemic equilibrium is obtained under certain restriction conditions.At the same time,some numerical simulations are given to verify our conclusions.Based on the second chapter,we make an attempt to study the global stability of the endemic equilibrium in a more general setting in this chapter.Firstly the global stability of the endemic equilibrium of one group SIR model is studied under different circumstances,by using the differential inequality and comparison principle,the area of the system ?-limits set is reduced.Then the global stability of the local disease equilibrium of two groups of SIR model is studied under certain condition.Finally,the results of theoretical analysis are verified by numerical simulation.