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Optimal Treatment of Prostate Cancer Based on State Constraint

Author

Listed:
  • Wenhui Luo

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China
    These authors contributed equally to this work.)

  • Xuewen Tan

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China
    These authors contributed equally to this work.)

  • Xiufen Zou

    (School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China)

  • Qing Tan

    (School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China)

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.

Suggested Citation

  • Wenhui Luo & Xuewen Tan & Xiufen Zou & Qing Tan, 2023. "Optimal Treatment of Prostate Cancer Based on State Constraint," Mathematics, MDPI, vol. 11(19), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4025-:d:1245506
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    References listed on IDEAS

    as
    1. Robert A. Gatenby, 2009. "A change of strategy in the war on cancer," Nature, Nature, vol. 459(7246), pages 508-509, May.
    2. C.Y. Kaya & J.L. Noakes, 2003. "Computational Method for Time-Optimal Switching Control," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 69-92, April.
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