A Clinical Applicable Optimal Control of HIV Using Discretization Scheme

ABSTRACT. Generally, to obtain a realistic optimal treatment strategy for Human Immunodeficiency Virus (HIV) infection, the amount of virus particles should be decreased and the amount of uninfected CD4+ T-cells must be increased. Since Nowak et al. have presented a mathematical model as an optimal control problem which involveds five kinds of viruses and cells (state variables) that discribe the dynamics of immune system, HIV and drug-resistant mutants, in this paper, a discretization method was used to convert the problem to a nonlinear programming one. Then, by solving this new problem, the optimal pair of control and states was obtained. Even the analytic solution of the nonlinear programming problem was perfectly acceptable but it was not suitable for physicians to apply. Therefore, by dividing the time interval to some subintervals and considering the control function as a piecewise constant function over these subintervals, a suboptimal control in therapy was obtained which was completely applicable for clinical purposes. Numerical simulations for both optimal and suboptimal strategies demonstrated that the obtained optimal treatments reduced the number of mutant virus particles and also increased the number of uninfected CD4+ T-cells count more than other optimal strategies.