Free End-Time Optimal Control Problem for Cancer Chemotherapy

The main motivation for this work is to determine the optimal dosage and duration for cancer chemotherapy that minimizes tumor cell number, treatment side effects, and therapy cost using optimal control theory for a model representing the interaction between immune and tumor cells with chemotherapy...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 33; no. 3; pp. 831 - 847
Main Authors Zouhri, Samira, EL Baroudi, Mohcine
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.07.2025
Springer Nature B.V
Subjects
Cancer
Chemotherapy
Computer Science
Control theory
Engineering
Mathematics
Mathematics and Statistics
Optimization
Original Research
Pontryagin principle
Runge-Kutta method
Side effects
Time optimal control
Tumors
Chemotherapy
Free end-time problem
Optimal control
Cancer
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Summary:The main motivation for this work is to determine the optimal dosage and duration for cancer chemotherapy that minimizes tumor cell number, treatment side effects, and therapy cost using optimal control theory for a model representing the interaction between immune and tumor cells with chemotherapy intervention. The optimal control problem with free end-time has been formulated and the optimal control characterization has been given using the Pontryagin’s maximum principle. The optimality system with a second transversality condition for the free end-time is added and solved numerically using a fourth order Runge–Kutta iterative approach and the iterative scheme of the gradient method. The results, with and without chemotherapy, are presented and discussed, and an optimal chemotherapy treatment strategy that has contributed to tumor elimination is suggested, along with the optimal treatment duration.
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ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-023-00654-x