Global Stability Of Infections Diseases Models With Saturation Infection And Humoral Immunity

Infectious diseases, which is caused by a virus, is a very common human diseases.Such as: HIV/AIDS, hepatitis B, infuenza, tuberculosis. In order to study the humanpopulation of infectious diseases. the researchers usually establish the appropriatemodel and analyze the model in theory and verify the theoretical results by numericalsimulations.In the frst chapter, we introduce background and the common theory of Math-ematical Biology, and give some preparing knowledge which are used in the paper.In the second chapter, we study the model with humoral immune and saturatedcontact rate. Using the Lyapunov function and LaSalle invariant set, the dynamicscharacter of the model was analyzed, meanwhile, some numerical simulations arecarried out to illustrate our analytic results.In the third chapter, we consider the above model with the discrete time delay. Bythe Lyapunov function, we obtain that the equilibria are the globally asymptoticallystable. Some numerical simulations are given to verify our theoretical results.In the fourth chapter, we presented and studied the model with saturated contactrate and showed the dynamics properties of the model. Some numerical simulationsare included.