HYBRID ON-OFF CONTROLS FOR AN HIV MODEL BASED ON A LINEAR CONTROL PROBLEM

Abstract

We consider a model of HIV infection with various compart- ments, including target cells, infected cells, viral loads and immune effec- tor cells, to describe HIV type 1 infection. We show that the proposed model has one uninfected steady state and several infected steady states and investigate their local stability by using a Jacobian matrix method. We obtain equations for adjoint variables and characterize an optimal control by applying Pontryagin's Maximum Principle in a linear control problem. In addition, we apply techniques and ideas from linear opti- mal control theory in conjunction with a direct search approach to derive on-off HIV therapy strategies. The results of numerical simulations indi- cate that hybrid on-off therapy protocols can move the model system to a healthy steady state in which the immune response is dominant in controlling HIV after the discontinuation of the therapy.