Stability Analysis of a Fractional Order Model of HIV virus and AIDS Infection in the Community

Abstract

In this paper a non-linear model with fractional order is presented for analyzing and controlling the spread of HIV virus. Both the disease-free equilibrium and the endemic equilibrium are found and their stability is discussed. The basic reproduction number , which is a function of the constant parameters in the model, plays an essential role in the stability of the above model. In more precise expression, When the disease-free equilibrium is attractor, but when , is unstable and the endemic equilibrium exists and it is an attractor. Finally numerical simulations are also established to investigate the influence of the parameters in the model on the spread of the disease.