Mathematical Analysis of a Non-Local Mixed ODE-PDE Model for Tumor Invasion and Chemotherapy

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.