Optimizing chemotherapy scheduling by iteratively solving a recurrence equation

We illustrate how an iterative method and the idea of recurrence can be employed to optimize chemotherapy scheduling. We take the density of host and cancer cells as the states, and aim at minimizing the treatment period for each state. We derive the equation satisfied by the optimal values of the objective function at different states. The theorem of existence and uniqueness for the solution to this equation is proved, and some important properties of the optimal values of the objective function are presented. The optimal treatment schedule can be derived directly from the optimal objective function values at different states. We use an iterative method to solve the equation numerically. Some ideas to further enhance the model are discussed.