A Study Of Infectious Disease Models With Latency And Delay

In this paper,infectious diseases of three classes are established and studied by using the related theory of differential equations.The article is divided into four 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.a class of SEIRS models with general incidence rate and influenza resistance are established and studied.Firstly,the basic reproductive number R0 is obtained by using the method of the spectral radius of regenerated matrix.Secondly,we discuss the stability of the equilibrium point by using the eigenvalue method and the Lyapunov function.We get the conclusion that if R0<1,the disease free equilibrium is globally asymptotically stable,and if R0>1,the endemic equilibrium is globally asymptotically stable under some conditions.Finally,numerical simulations are provided to support our theoretical results.In Chapter 3,a class of SIRD time delay model for Ebola disease with general incidence rate and vaccination are established and studied.For the model without delay,we get that if R0<1,the disease-free equilibrium is globally asymptotically stable,whereas if R0>1.the endemic equilibrium is globally asymptotically stable.Further,we incorporate a time lag in the model and find that.the delay does not affect the overall dynamics of the system.Numerical simulations are carried out to explain the mathematical conclusions.In Chapter 4.a class of delay model with virus waning terms and HBV DNA-containing capsid are established and studied.Firstly,we calculate the basic reproduction number R0 and the existence of the equilibrium point.Secondly,when time delay ? = 0,the disease free equilibrium and endemic equilibrium stability is discussed.Further,the critical value of delay?0 is obtained,and when the delay increases through ?0,the stability of the endemic equilibrium point of the model is changed and the Hopf bifurcation is generated.By applying the normal form method and center manifold theorem,we also derive some explicit formulae determining the bifurcation direction and the stability of the bifurcated periodic solutions.Finally.numerical simulations are provided to support our theoretical results.