Stability analysis for fractional differential equations of an HIV infection model with cure rate

In this paper, we introduce a fractional differential HIV/AIDS infected model with Beddington-DeAngelis functional response rate. Moreover as for a feature, we consider cure rate of infected CD4 T cells. We show that the model introduced in this paper has nonnegative solutions which are all bounded. What is more, we also give a detailed analysis for the asymptotic stability of both the free equilibrium and the infected equilibrium. We have proven that if the basic reproduction number R0 is less than unity, then the disease-free equilibrium is locally asymptotically stable. If R0 is greater than unity, the infected equilibrium is locally asymptotically stable under some conditions.