Study of a system of non-linear difference equations arising in a deterministic model for HIV infection

A deterministic model for HIV infection in the presence of combination therapy is introduced. The model is then approximated by an implicit finite-difference method, a system of difference equations, to solve the IVP system. We initially purpose the discrete analogue of the continuous model of HIV infection. Then the boundedness, the local and the global asymptotic stability of the equilibria of the system of difference equations, the bistability phenomenon, and the bifurcation phenomenon are also investigated. In addition, we will show that the associated approximational method is very robust since the equilibria and the stability conditions are independent on the time step. Finally numerical simulations of the system are presented when the system has meaningless solutions in view point of biology or our theory is incapable.