We present a new mathematical model for acid-mediated tumor invasion encompassing chemotherapy treatment. The model consists of a mixed ODE-PDE system with four differential equations, describing the spatio-temporal dynamics of normal cells, tumor cells, lactic acid concentration, and chemotherapy drug concentration. The model assumes non-local diffusion coefficients for tumor cells. We provide an analysis on the existence and uniqueness of model solutions. We also provide numerical simulations illustrating the model behavior, showing the invasion and the treatment phases, and comparing the model solutions with the case of constant diffusion coefficients instead of the non-local terms.

我们提出了一种新的数学模型，用于酸介导的肿瘤浸润，包括化学疗法的治疗。该模型由具有四个微分方程的混合ODE-PDE系统组成，描述了正常细胞，肿瘤细胞，乳酸浓度和化疗药物浓度的时空动态。该模型假设肿瘤细胞的非局部扩散系数。我们对模型解的存在性和唯一性进行了分析。我们还提供了数值模拟，说明了模型的行为，显示了侵入和处理阶段，并将模型解与恒定扩散系数而不是非局部项的情况进行了比较。