Dynamic Behavior Analysis And Optimal Control Research Of Two HIV Models

AIDS caused by HIV infection is a highly harmful infectious disease worldwide.HIV mainly attacks the CD4+T cells which are the most important cells in the human immune system and ultimately destroys the human immune system completely.Therefore,it is nec-essary to establish a mathematical model to understand the HIV progress in infected indi-viduals and to formulate the best drug treatment strategy.This paper studies two special HIV models,discusses the dynamic behaviors of these models,uses optimal control theo-ry to find the most suitable control strategy,and reduces the harm of the virus as much as possible while reducing the cost of treatment.The main structure of this paper is as follows:The first chapter,introduces the research background of HIV,the status of related re-search and development of HIV mathematical models,as well as the main work and inno-vations of this paper.The second chapter,introduces related definitions,lemmas and theorems in dynamic system and optimal control theory.The third chapter,studies the dynamic behavior and optimal control of a HIV model that considers drug intervention and CTL immune response and has a nonlinear incidence.Firstly,we prove the non-negativity and boundedness of the solution,use the regeneration matrix method to obtain the basic regeneration number R₀,and give the expression of the CTL immune regeneration number R₁,at the same time discuss the existence of equilibrium points.Next,it is proved that the disease-free equilibrium point is globally asymptotically stable when R₀<1,the disease equilibrium point without immune response is globally asymptotically stable when R₁<1<R₀and the immune equilibrium point is globally asymptotically stable when R₀>1,R₁>1.Simultaneously,we verify the stability of the equilibrium points through numerical simulation.Finally,we add the dynamic control of three drugs to the model,prove the existence of the optimal control,and use the Pontryagin maximum principle to find the expression of the optimal control.The fourth chapter,studies the dynamic behavior and optimal control of a type of HIV model with non-linear incidence and considering the absorption term.Firstly,we give the non-negativity and boundedness of the solution of the model,and discuss the existence of the three equilibrium points of the model,then give sufficient conditions for the local asymptotic stability of the equilibrium points mainly by the Routh-Hurwitz theorem,finally add the control terms of the action of two drugs to the model,prove the existence of the optimal control and use the Pontryagin maximum principle to obtain its specific expression.The fifth chapter,summarizes the content of this paper and points out the direction of future efforts.