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arXiv · 2212.05146

On a Mathematical Model Arising from an Optimal Chemotherapeutic Drug Treatment for Tumor Cells

Hong-Ming Yin
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Abstract

In this paper we consider an optimal control problem arising from a chemotherapeutic drug treatment for tumor cells in a living tissue. The mathematical model for the interaction of chemotherapeutic drug and the normal, tumor and immune cells are governed by a nonlinear reaction-diffusion system. We first establish the well-posedness for the nonlinear system. Then we study the long-time behavior of the solution for the model problem. Finally, we design an optimal drug dosage, which leads to an optimal control problem under certain constrains. A complicated factor for the optimal control problem is that a minimum level of normal cells in patients must be maintained during a treatment. It is shown that there is an optimal drug dosage for the chemotherapeutic treatment for patients.

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Hong-Ming Yin. 2022-12-09. On a Mathematical Model Arising from an Optimal Chemotherapeutic Drug Treatment for Tumor Cells. https://arxiv.org/abs/2212.05146

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