Multiobjective Optimal Control of HIV Dynamics

Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized, and a multiobjective optimal control problem MOOCP is proposed to maximize the CD4 T cells population and minimize both the viral load and drug costs. The weighted sum method is used, and continuous Pareto optimal solutions are derived by solving the corresponding optimality system. Moreover, a model predictive control MPC strategy is applied, with the final goal of implementing Pareto optimal structured treatment interruptions STI protocol. In particular, by using a fuzzy approach, the MOOCP is converted to a single-objective optimization problem to derive a Pareto optimal solution which among other Pareto optimal solutions has the best satisfaction performance. Then, by using an embedding method, the problem is transferred into a modified problem in an appropriate space in which the existence of solution is guaranteed by compactness of the space. The metamorphosed problem is approximated by a linear programming LP model, and a piecewise constant solution which shows the desired combinations of reverse transcriptase inhibitor RTI and protease inhibitor PI drug efficacies is achieved.