Stability And Optimal Control Of Several Types Of Infectious Disease Models

In this paper,we consider global stability and optimal control of several kinds of infection models with two immune response（cell-mediated immune response and humoral immune response）.We consider the global stability of infection models via Lyapunov function method and LaSalles invariance principle and analyze the dynamic nature of infection models,then use Hamilitonian function and Pontryagin’s maximum principle to investigate the optimal control of infection models.Through the study of infection models,several new result are obtained based on the existed later reture.This paper is divided into four chapters according to the content.Chapter 1,We introduce the background of the problems and the main contents of this paper.Chapter 2,We study the global dynamics and optimal control of HIV infection model with Bedding-DeAngelis incidence rate and CTL immune response.We construct Lyapunov function to study the global dynamic nature of different equilibriums.If R₀< 1,the infection-free equilibrium point E₀ is global asymptotically stable.If R₁< 1 < R₀,the immune-free equilibrium point E₁ is global asymptotically stable.If R₁> 1,the endemic equilibrium point E₂ is global asymptotically stable.We construct objective functional,then defined the Hamilitonian function and use Pontryagin’s maximum principle to prove existence of an optimal control pair and obtain the expression of optimal control pair.Chapter 3,We study optimal control of an epidemiological model with multiple time delays and bilinear incidence rate.In this section,on the basis of the epidemiological model of Eihab B.M.Bashier,we consider optimal control problems of an epidemiological model with multiple time delays and bilinear incidence rate.At the same time,we consider two different control strategy u（t）andv（t）,respectively,the two functions u（t）andv（t）represent vaccination strategy and treatment strategy.We construct objective functional,then defined the Hamilitonian function and use Pontryagin’s maximum principle to prove existence of an optimal control pair and obtain the expression of optimal control pair.Chapter 4,We study optimal control of a delayed HIV infection model with cytotoxic T-lymphocyte and antibody responses.At first,we prove that all the solution of the infection model are positivity and bounded.then we obtain equilibriums and find basic reproductive number.We construct objective functional,then defined the Hamilitonian function and use Pontryagin’s maximum principle to prove existence of an optimal control pair and obtain the expression of optimal control pair.