Study On The Stability And Application Of Two Classes Of HIV/AIDS Dynamical Models

Two classes of HIV/AIDS infectious disease dynamics models were proposed and studied in this paper,and the application of HIV/AIDS infection control was studied by means of dynamics method,and the comprehensive preventive and intervention strategies for HIV/AIDS infection control were obtained.On the basis of analyzing the data of HIV/AIDS infection in Hunan Province,the strategies to prevent and control the further epidemic of HIV/AIDS were put forward,and the possible epidemic situation of the disease in Hunan Province was predicted in the future.There were five chapters in this paper.In the first chapter,we introduced the research background,the relevant domestic and foreign research results and the main research contents.In the second chapter,we put forward a class of fractional HIV/ AIDS epidemic model with horizontal inhibition and mother-to-child vertical transmission,and the parameter expression of basic reproduction number was given.Then,the disease-free equilibrium and the endemic equilibrium were obtained,and the conditions for the local asymptotic stability of the two kinds of equilibrium points were proved.Finally,we used the numerical simulation method to verify the correctness of the theoretical proof and made some relevant analysis.The results showed that: safer sex based on promoting condom use,more effective testing of HIV antigen in blood and blood products,and continuous use of clean needle exchange were the basis for controlling HIV/AIDS infection.In the third chapter,we had studied a class of HIV/ AIDS epidemic model with screening and new media influence factors,and the parameter expression of basic reproduction number was obtained by using the next generation matrix.Next,the local asymptotic stability of the two types of equilibrium points was proved by the correlative theory,and the global asymptotic stability of the disease-free equilibrium was proved by constructing Liapunov function.In the end,the effects of different parameters combinations on the spread of disease were studied by numerical simulation in five different cases.The results showed that: giving full play to the role of new media to decrease the efficiency of HIV transmission through sexual transmission,blood transmission and increasing screening rate can effectively reduce or even eliminate HIV infection in the population.In the fourth chapter,we analyzed the current situation of HIV/AIDS infection in Hunan Province,used the dynamic model method to fit the infection situation,and got a set of parameters which fitted well with the actual situation.Based on the results of dynamic analysis,we put forward some suggestions to prevent the further epidemic of disease,and forecast the possible epidemic situation of disease in Hunan Province in the future.In the fifth chapter,we summarized and discussed the research of this paper.