abstrak Human Immunodeficiency Virus (HIV) is one of the virus which attacks human immunity and causes AIDS. This virus spreads quickly and has a great mortality rate. Therefore, it is important to study the spreading of the HIV, especially in homosexual populations because the spreading of the HIV started in it. The purposes of this research are to analyze the stability of the equilibrium point and to give the interpretation of the result in the example. The research uses literary study. The steps to find the goal are determining the equilibrium point, analizing the equilibrium and the stability of the model. The stability is analyzed by Routh-Hurwitz Criterion. As the conclusion, the spreading of HIV model can be divided into model without blood screening and model with blood screening. Each model has two free equilibrium points. Those equilibrium points will be stable if the reproduction ratio 1 0 < R>
