Abstract
Mathematical modeling can describe about how the epidemic model like virus HIV/AIDS interaction with human, from susceptible individual become individual AIDS. Furthermore, the model is built in the acceleration fraction how fast susceptible individuals can be asymptomatic HIV infected individuals. It can be solved to get the point of free disease and its stability, and also to get endemic point and its stability. The stability for the free disease will get from the Routh's criterion stability, and for the endemic will be analyzed by Lyapunov function. In the paper, the point of free disease will be asymptotically stable if the basic reproduction of the model less than one, and the point of endemic will stable with Lyapunov if the basic reproduction more than one.
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