The Study Of HIV Models With Bridge-people

Mathematical models and dynamical analysis are important methods in the study of infectious diseases.According to the spread characteristics of HIV/AIDS, this paper builds an HIV differential equation model which has bridge-people. In the interior, we build the ID model; after adequate study of it, we get our conclusions, which not only enriches the literatural results, but also endows more significance to prevention and control of AIDS.Firstly, we introduce the HIV/AIDS problems, the HIV/AIDS mathematical models and the present situation of research. Later we give a sketch of the major contents and frame in organization.Secondly, we build an HIV model with bilinear incidence. Then we give the reproduction number, and prove the global asymptotic stability of the infection-free equilibrium and local asymptotic stability of the endemic equilibrium. Compared with other documents which deal with the same model, our study is more complete.Thirdly, we study the HIV model with standard incidence. We also give the basic reproductive number, and prove the global asymptotic stability of balance points in non-disease occasion and local asymptotic stability of balance points in local-disease occasion.Lastly, for the HIV model with standard incidence rates, we study the persistence at the endemic equilibrium. Consequently we conclude that AIDS will always exist under certain conditions.