Optimal Treatment of Prostate Cancer Based on State Constraint

As a new tumor therapeutic strategy, adaptive therapy involves utilizing the competition between cancer cells to suppress the growth of drug-resistant cells, maintaining a certain tumor burden. However, it is difficult to determine the appropriate time and drug dose. In this paper, we consider the competition model between drug-sensitive cells and drug-resistant cells, propose the problem of drug concentration, and provide two state constraints: the upper limit of the maximum allowable drug concentration and the tumor burden. Using relevant theories, we propose the best treatment strategy. Through a numerical simulation and quantitative analysis, the effects of drug concentrations and different tumor burdens on treatments are studied, and the effects of cell-to-cell competitive advantage on cell changes are taken into account. The clinical dose titration method is further simulated; the results show that our therapeutic regimen can better suppress the growth of drug-resistant cells, control the tumor burden, limit drug toxicity, and extend the effective treatment time.