Optimal Control in a Model of Chemotherapy-induced Radiosensilisation

  In this work, we consider a simple mathematical model of radiochemotherapy which includes a term responsible for radiosensitization. We focus on finding theoretically optimal controls which maximise tumour cure probability for a finite, fixed therapeutic horizon. We prove that the optimal controls for both therapies are of 0-bang type, a result which is not altered by the inclusion of the radiosensilization term. By means of numerical simulations, we show that optimal control offers a moderate increase in survival time over a sequential treatment. We then revisit in more detail a question of measuring the synergy between the therapies by means of isobolograms, a common experimental technique for measuring the additivity of two treatments.