Global Stability and Sensitivity Analysis of SIA Model for AIDS Disease

Abstract

Over the years, cases of HIV and AIDS spread throughout Indonesia and continue to increase. This is becoming a serious concern so it requires a management or strategy to reduce its spread. In this article, a simple mathematical model will be built that represents HIV AIDS cases in general. The population assumed to be closed population and consisted of SIA (Susceptible, Infected, and AIDS case) population. Furthermore, this model will be analysed through basic reproduction number (0), global stability using Lyapunov function, and also sensitivity analysis from each parameters. The result of analysis and simulation shows that the rate contact between susceptible and infected is one of the most influential parameters in the spread of AIDS.