On the Behavior of Numerical Solutions with Natural of Stability and Controllability of Viral Dynamical Models

The system of differential equationsfor simple mathematical models of Human Immune-deficiency Virus (HIV)for the model which components are plasma densities of uninfectedCD4+T helper cells, infectedCD4+Thelper cells and free virus (HIV-1) will be study within the nature of equilibrium points and discuss stability for each of them. After that we study controllability using therapy that uses constant drug dosage of reverse transcription inhibitor (RTI) and protease inhibitor (PI) to help HIV– infected patient to achieve long term non-progressor (LTNP) status. Also, observability and output controllability will apply on this model where in general the state controllability is neither necessary nor sufficient for controlling the output. The analytical treatments are complemented with the numerical solution of the system.