Computation, Modeling, and Simulation of HIV-AIDS Epidemics with Vaccination

Abstract

The principles of the HIV-AIDS epidemics are established based on the subpopulation 1) Susceptible; 2) HIV-infected; 3) AIDS-infected; 4) Immunized. The immunized subset of the population in this paper is the total individuals who were infected and cured or immunized by vaccination. The immunized group can be identified by removing individuals from the susceptible group. A general mathematical model is developed for HIV-AIDS epidemics with Vaccination to understand the spread of the virus throughout the population. Particularly we use numerical simulation with some values of parameters to predict the number of infected individuals during a certain period in a population and the effect of vaccine to reduce infected group and increase the number of immunized individuals. Further, we expand the research to special cases with no vaccinations. A special case is 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, one can reduce four-stage HIV-AIDS investigation to a three-stage of SIR. With this introduction and modification, the numerical simulation can be developed the Monte Carlo simulation method in SIR case to verify the Validity of the HIV-AIDS model.