Control of immune response of HIV infection model by gradual reduction of drug dose

It is known that HIV (human immunodeficiency virus) infection that causes AIDS is a dynamic process that can be modeled mathematically. By changing the drug effect in the model, which can be regarded as the control input, the control goal of this paper is to drive any initial state into an equilibrium called the ´non-progressor,´ where the symptom of infected patient will not be developed into AIDS. A new treatment idea is proposed which can be simply stated as ´slow reduction of dose after the maximum dose for a period´. This idea is guaranteed to work through mathematical proofs. In particular, we prove the proposed scheme by analyzing the model in view of positively invariant set, non-vanishing basin of attraction with respect to the constant drug dosage, and stability under slowly varying input. We also present a set of conditions on the parameters, which characterizes the model to which the proposed treatment is applicable. In summary, we prove global asymptotic controllability of the equilibrium of non-progressor under the proposed conditions on parameters.