Stability Analysis And Optimal Control Of HIV/AIDS Epidemic Models With Awareness And Sexual Transmission

AIDS is a kind of infectious disease with great harm all over the world.The dynamics model of HIV/AIDS can predict the development trend of HIV/AIDS and assist in the formulation of reasonable control strategies,which is currently one of the hot issues in relevant researches in biomathematics.Using differential equations to simulate the spread of HIV/AIDS can reveal some significant problems in its spread process,such as the existence and stability of endemic equilibrium points and the disease-free equilibrium points,etc.In this paper,two kinds of differential equation models of HIV/AIDS are discussed.The stability of the equilibrium points of the models and the optimal control of the second model are analyzed.The first chapter briefly introduced the research meaning and the research actuality of this paper.The second chapter provided a series of preliminary knowledge about the stability of differential equations and optimal control theory.In the third chapter,an HIV/AIDS epidemic model with awareness and sexual transmission was considered.We obtained the existence of disease-free equilibrium points and endemic equilibrium points and proved their stability.In the fourth chapter,an HIV/AIDS epidemic model with awareness,control strategy and sexual transmission was considered.We not only proved the existence and stability of endemic equilibrium points and the disease-free equilibrium points,but also discussed the optimal control problem of the model.The purpose of discussing the optimal control problem is to select an optimal control scheme,which can not only minimize the control cost,optimize the allocation of resources,but also minimize the number of infected people.