论文标题
在由肿瘤细胞最佳化学治疗治疗的数学模型上
On a Mathematical Model Arising from an Optimal Chemotherapeutic Drug Treatment for Tumor Cells
论文作者
论文摘要
在本文中，我们考虑了由活组织中肿瘤细胞的化学治疗药物治疗引起的最佳控制问题。化学治疗药物与正常，肿瘤和免疫细胞相互作用的数学模型受非线性反应扩散系统的控制。我们首先建立了非线性系统的适合性。然后，我们研究模型问题解决方案的长期行为。最后，我们设计了一种最佳药物剂量，这在某些约束下导致最佳控制问题。最佳控制问题的一个复杂因素是，在治疗过程中必须保持患者的最低正常细胞水平。结果表明，患者的化学治疗治疗有最佳的药物剂量。
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.
