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Mathematical model of optimal control for endometrial cancer with treatments dostarlimab and chemotherapy using Caputo derivative

Kalimuthu Ramalakshmi,M. Samei

Published 2025 in Scientific Reports

ABSTRACT

We develop a mathematical model to investigate endometrial cancer progression and treatment response under dostarlimab and chemotherapy using nonlinear ordinary differential equations (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {ODE}$$\end{document}s), and extend the framework to fractional differential equations (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FDE}$$\end{document}s) with the Caputo derivative to capture memory effects. Existence and uniqueness of solutions are established via the Banach fixed-point theorem, and stability analysis is performed using the Routh–Hurwitz criteria. An optimal control framework is formulated to evaluate single and combined therapies under both \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {ODE}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FDE}$$\end{document} settings. Numerical simulations are carried out in MATLAB, employing the ode45 solver for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {ODE}$$\end{document} systems and the fde12 solver for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FDE}$$\end{document} systems. Results indicate that dostarlimab monotherapy is more effective than chemotherapy alone, while combined therapy achieves the greatest reduction in cancer cells and the strongest activation of CD8+ T-cells. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {ODE}$$\end{document} model provides faster tumor reduction and higher immune activation, whereas the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FDE}$$\end{document} model achieves lower overall therapeutic cost by balancing tumor reduction with reduced drug usage. These findings highlight the potential of optimal control strategies particularly combined therapy for improving treatment outcomes in endometrial cancer management.

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