Novel Model of HIV-AIDS Epidemics with Vaccination

The principles of the HIV-AIDS epidemics and the relations of susceptible, HIV infected, AIDS, and immunized subpopulation will be established. We would like to develop a general mathematical modeling for HIV - AIDS with Vaccination to understand the spread of the aids virus and to predict the number of infected individuals during a certain period in a population. Further we expand the research to special cases with no vaccinations. We will investigate the model in special case when the removal subset of the population is empty, or there is no recovery in this epidemic. We also can consider the total infected number is equal to the sum of the HIV infected and the number of AIDS infected. As a result, we can use SIR Monte Carlo simulation method in SIR case to verify the Validity of the HIV-AIDS model.