Optimal Treatment of Prostate Cancer Based on State Constraint

Wenhui Luo, Xuewen Tan (), Xiufen Zou () and Qing Tan
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Wenhui Luo: School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China
Xuewen Tan: School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China
Xiufen Zou: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
Qing Tan: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Mathematics, 2023, vol. 11, issue 19, 1-17

Abstract: 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.

Keywords: problems in pharmacology; drug toxicity; tumor burden; state constraints; optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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