Qualitative Analysis Of Several Epidemic Models

This thesis mainly studies a SEIR epidemic model with vertical transmission, a nonautonomous SEIR epidemic model with vertical transmission,and a nonautonomous SEIR epidemic model with vertical transmission and variation of population.It is consists of four chapters.As the introductions,in Chapter 1,the background and history of epidemic model are briefly addressed,and the main work of this paper are given.In Chapter 2,We discusse a SEIR epidemic model with vertical transmission and obtain the threshold value R₀^* of the endemic equilibrium.When R₀^*＜1,there only exists disease free equilibrium and it is local asymptotic stable;When R₀^*＞1,there not only exists unstable disease free equilibrium,but also exists positive endemic equilibrium and it is local asymptotic stable.In Chapter 3,a nonautonomous SEIR epidemic model with vertical transmission is studied.Under quite weak assumptions,we not only have established the sufficient condition on the uniformly strong persistence of the disease,but also obtained the sufficient condition on the extinction of the disease.In Chapter 4,a nonautonomous SEIR epidemic model with vertical transmission and variation of population is studied.Under quite weak assumptions,we not only have established the sufficient condition on the uniformly strong persistence of the disease,but also obtained the sufficient condition on the extinction of the disease.