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 radiosensilisation. We focus on nding theoretically optimal controls which maximise tumour cure probability for a nite, xed therapeutic horizon. We prove that the optimal controls for both therapies are of 0-bang type, a result which is not altered by inclusion of the radiosensilisation term. By means of numerical simulations we show that optimal control oers 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 additivity of two treatments.