Research Of Two Types HIV/AIDS Epidemic Fractional Models

Two types of mathematical HIV/AIDS transmission models based on fractional differential equations are discussed in this thesis.The models have took account of human awareness and intervention measures factors to the transmission of the HIV/AIDS epidemic.We discussed the existence of the equilibrium points of the models and their stability to support our theoretical result.The thesis is divided into five chapters:In Chapter 1,we give a brief introduction of the research status and the research significance on the mathematical models of the HIV/AIDS epidemic.The results obtained in this thesis are also presented here.In Chapter 2,introduce some definitions and preliminary facts needed in the following chapters are given.In Chapter 3,taking human awareness factors during disease transmission into consideration,we establish a class of HIV/AIDS epidemic fractional differential models.The existence of the equilibrium points of the models and their stability are discussed.The numerical modeling verified the theoretical result.In Chapter 4,a class of HIV/AIDS epidemic fractional differential models with awareness and intervention measures is established.The existence of disease-free equilibrium points and endemic equilibrium points is discussed and their stability is proved.The research finds out that stronger intervention measures will reduce the transmission of HIV/AIDS.In Chapter 5,some remarks on our work in this thesis and several possible problems which can be viewed as our future work are given.