Studying a fractional order model to investigate the effect of drug treatment on HIV control

In this paper, a fractional order model is presented to study the effect of the drug therapy on the control of HIV infection. For this purpose, we calculate the reproduction number of the model with the next generation operator method and by using that, we study the stability of equilibrium point. Reproduction number $R_0$ plays an important role in spreading or non-spreading of HIV. So that, if $R_0 < 1$, the infection-free equilibrium point is locally asymptotically stable and the infection is cleared from the $CD{4^ +}T$-cell population. In the res, we analyze the relationship between the reproduction number and the therapy parameter values, for some different values of the order of model. Also, we evaluate the effect of the therapy parameter on the immune system cells and HIV virus population. Finally, we simulate the variations of one of the parameters that show the amount of virus production by actively infected cells. Adams predictor-corrector method will be used to solve the fractional order model.