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

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.