The Study Of An HIV/AIDS Epidemic Model With Sexual Transmission

Infectious diseases harm to human health and damage the national economy.In re-cent years,the spread tendency of HIV/AIDS has shown new changes.Sexual contact has become the dominant transmission mode of the epidemic.Among HIV/AIDS sexu-ally infected cases,the growth of male-to-male sexual transmission is very significant in China.The proportions of male and female HIV/AIDS infected people is different,the transmission rate of male to female and female to male is also different,thus it needs to consider the people indifferent sex groups.This paper consists of three parts.First part is the introduction,which deals with the background,current status and significance of the mathematical study of HIV/AIDS epidemic.Second part is the preliminaries,which introduces basic theorems related to our study.Third part is three different mathematical model consider the HIV/AIDS epidemic.The first model is an HIV/AIDS epidemic model with sexual transmission considers of both heterosexual and homosexual(Male-to-Male)transmission.We analyzed basic properties of the model,including non-negativity and boundlessness.In accordance with earlier works,we calculated the basic reproduction number,RO,by using next generation method.What's more,using the comparison principle and the geometrical approach,we get the global asymptotic stability of disease-free equilibrium when R0<1 and globally asymptotically stability of endemic equilibrium when R0>1,separately.We give some numerical simulations using MATLAB and data from the east lake area of Nangchang city,to verify our results.The second model is an HIV/AIDS epidemic model with direct inflow of other new infected persons considers the migration of infected persons.Firstly,we give some ba-sic amuses and analyzed basic properties of the model,including non-negativity and boundlessness.In accordance with earlier works,Using next generation method,we get the basic reproduction number,RO.Secondly,using the comparison principle and the geometrical approach get the global asymptotic stability of disease-free equilibrium and endemic equilibrium,separately.Our numerical findings are illustrated through comput-er simulations using MATLAB.Finally,the basic model is extended to include several control efforts aimed at reducing infection and changing behavior.We use Pontryagin's maximum principle to derive the optimum system and solve the system numerically.Publicity education,testing and screening is the major control strategies.We give some numerical simulations using MATLAB and discuss relevant control strategies.The third model is an HIV/AIDS epidemic model with the incidence of general and different virus latency.At first,we analyzed non-negativity and boundlessness of model,and get the positively invariant set of system.The next,using zero-point theorem,we proved existence of positive equilibrium of the system.And using next genera-tion method,we calculated the basic reproduction number,RO.we defined structure of Liapunov functions and use LaSalle's invariance principle to discuss the global asymp-totic stability of the equilibrium point.Finally,we give some numerical simulations using MATLAB and choose the bilinear of standard.