Bang-bang optimal controls for a mathematical model of chemo- and immunotherapy in cancer
Urszula Ledzewicz, Helmut Maurer, Heinz Schättler, Dept. of Applied Mathematics, Westfälische Wilhelms Universität Münster, 48149 Münster, Germany
Abstract
A nonlinear mathematical model which includes synergistic effects of chemo- and immunotherapy is analyzed (both analytically and numerically) as an optimal control problem with free terminal time for the problem of scheduling combination therapies. Side effects of the drugs are measured indirectly by including the total doses of the respective drugs with weights as penalty terms in the objective. The formulation allows us to judge the amounts of the agents required to achieve tumor eradication as well as the time it will take to do so. For various weights for the penalty terms, extremal controlled trajectories are computed numerically and their local optimality is verified with second-order conditions for optimality.