Optimal hybrid on-off controls for an HIV model

초록

In this talk, we consider a model of HIV infection with various compartments, including target cells, infected cells, viral loads and immune effector cells, to describe the human immunodeficiency virus(HIV) type 1 infection. We show that the proposed model has one uninfected steady state and two infected steady states and investigate their local stabilities by using a Jacobian matrix method. In addition, we apply techniques and ideas from linear optimal control theory in conjunction with a structured treatment interruption( STI) control to derive optimal on-off HIV therapeutic strategies. We obtain the equations for the adjoint variables and the characterization of optimal control function by applying the Pontryagin’s Maximum Principle. The results of numerical simulations indicate that the optimal 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 discontinuation of therapy.