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DOI: 10.23952/cot.2026.38
Received April 14, 2025; Accepted July 27, 2025; Published online May 1, 2026
Abstract. Current prostate cancer treatment protocols, based on continuous use of the maximum tolerated dose of an anticancer drug, rapidly destroy drug-sensitive cancer cells in the patient’s body. As a result, they change the competition between drug-sensitive and drug-resistant cancer cells in favor of the latter. As drug-resistant cancer cells begin to dominate in the patient’s body, continued therapy may become ineffective. A new direction in prostate cancer treatment is adaptive therapy. It allows a significant number of drug-sensitive cancer cells to survive using only minimally effective doses of drugs with temporary breaks in drug administration. As a result, drug-sensitive cancer cells compete for common limited resources and suppress the proliferation of drug-resistant cancer cells. Finding optimal moments for switching between dosing and resting intervals by monitoring patient characteristics in real time is critical for the success of adaptive therapy. In this paper, for a given time interval representing the total period of prostate cancer treatment, the corresponding Lotka-Volterra mathematical models describing the competition between drug-sensitive and drug-resistant cancer cells during adaptive therapy are investigated, taking into account both the direct and indirect effects of the targeted drug. These models contain time control functions that are responsible for switching between the stage of active adaptive therapy to the stage of its absence and vice versa. To find the optimal moments of switchings, it is necessary to minimize the total load of cancer cells both during the entire period of prostate cancer treatment and at its final moment. The optimal control problems are solved using the Pontryagin maximum principle and the non-oscillatory theory of differential equations. The optimal scenarios of drug administration are obtained analytically. The results are discussed.
How to Cite this Article:
E. Grigorieva, E. Khailov, Controlled Lotka-Volterra competition models in adaptive therapy of prostate cancer, Commun. Optim. Theory 2026 (2026) 38.