Modeling Of HIV/AIDS Transmission And Its Analysis

AIDS(Acquired Immunodeficiency Syndrome), as one of the most dangerous infectious diseases, has been spreading at an enormous speed to all regions of the world. The urgent task facing the human is to elaborately investigate HIV/AIDS in the fields of epidemiology, immunology, social psychology and so on. Mathematical modeling the transmission and dynamics of HIV/AIDS infection can lead to a deeper understanding of disparate experimental data and identify therapies most likely to be effective in controlling the disease.In the present paper, a dynamic HIV/AIDS model with vertical transmission, infection-age, AIDS-age and the role of individuals with AIDS in HIV transmission is formulated. An imperfect vaccine with therapeutic effect is assumed, which induces reversal from the AIDS stage to the asymptomatic stage. In the past models, the aspects of vertical transmission, the role of individuals with AIDS in HIV transmission and the recovery rate of the individuals, who are in the AIDS stage, are usually ignored. The model is coupled by equations of differential equations and integral equations, where, differential equations include partial differential equations and ordinary differential equations. Furthermore, infection-age is included in the stage of latent period and the AIDS-age is used in the stage of AIDS. By the HIV/AIDS model, the conclusion is that the total population is decreasing when the mortality rate is increased by AIDS.In order to comprehend the effect of HIV/AIDS on the population, we analyze the linear equations when the birth rate is the same as natural mortality rate. By using the method of functional analysis, especially the linear operator and C₀ semigroup theory on Banach space, we prove well-posedness of the solution and existence of the positive solution.