Optimal drug application on stochastic cancer growth: an approach through path integral control

Abstract: We provide an overview of an optimal control problem within a stochastic model of tumor growth, which includes drug application. The model comprises two stochastic differential equations (SDE) representing the diffusion of nutrient and drug concentrations. To account for various uncertainties, stochastic terms are incorporated into the deterministic framework, capturing random disturbances. Control variables, informed by medical principles, are used to regulate drug and nutrient concentrations. In defining the optimal control problem, a stochastic cost function can be established, and a Feynman-type path integral control approach would lead to an optimal drug treatment.