OPTIMAL CONTROL STRATEGY FOR IMPROVED BIOCHEMOTHERAPY OUTCOME IN CANCER PATIENTS’ TREATMENT

Abstract

Cancer is a serious medical problem globally, thus efforts to combat the scourge is a continuous one. Here, a deterministic mathematical model for cancer cells’ dynamics in the presence of biochemotherapy is considered. The model is a system of coupled ordinary differential equations (ODEs) which describes cancer cells’ growth on a cell population level under the influence of biochemotherapy. The proposed model solution is shown to be positively invariant and bounded. Thereafter, the scenario for the administration of the therapy is formulated as an optimal control problem subject to the proposed model dynamics with the goal of obtaining the optimal levels of each of the treatment regimen that must be adopted in order to minimize the number of cancer cells as well as the therapy toxicity while maximizing the immune system performance. The optimality system for the optimal control problem is derived based on Pontryagin’s Maximum Principle and the resulting system is solved numerically with fourth order Runge-Kunta scheme using forward-backward sweep approach. Simulations of the numerical results were carried out. Different combinations of therapy effectiveness and toxicity levels were examined. Findings from the simulations show that therapy outcome depends not only on the effectiveness of the therapy but also on its adverse effect which could vary across patients. Moreover, the outcome of the therapy absolutely depend on the cancer cells population when the biochemotherapy is initiated. Nevertheless, it was found that biochemotherapy could effectively and remarkably curtail the growth of the cancer cells within a reasonable short time, if the therapy is timely initiated.