OPTIMAL-CONTROL DRUG SCHEDULING OF CANCER-CHEMOTHERAPY

This optimal control model of cancer chemotherapy constructs drug schedules that most effectively reduce the size of a tumour after a fixed period of treatment has elapsed. A constraint is imposed so that the tumour size must decrease at or faster than a specified rate. The system is solved using an established numerical solution technique known as control parametrization, and analytical gradients are constructed of all the constraints so that the resulting non-linear programming problem is solvable using currently available software. An interesting feature of the constraints on the rate of decrease of the tumour size is that the corresponding co-state functions are discontinuous in time. Numerical solutions suggest that the best way of reducing the tumour burden after a fixed period of treatment is to keep the rate of decrease of the tumour size to a minimum initially, and then give high-intensity treatment towards the end of the treatment period.