Epidemic Models With Recruitment Rate And Nonlinear Incidence Rate

In this paper, we study epidemic models with recruitment rate. Theasymptotic behavior of solutions of the systems are analyzed. The article is divided into four chapters.In Chapter 1, we give the background of this paper and the literature review.In Chapter 2, we study two epidemic models with treatment function.We obtain the sta-blity and existence of the equilibriums,and the sufficient condition of the backward bifurcation existence is obtained.In Chapter 3, we study a class of SIR epidemic model with virus auto variation. thresholds have been established,in theroy, we put forward that the sharp threshold condition exists.We prove the globally stablity of the equilibriums by constructing Liapunov functionand and using Lasalle theory.In Chapter 4, we study a class of epidemic model with vaccination and isolated items. The globally stablity of the disease-free equilibrium and endemic equilibrium is obtained.