On a Reaction-Diffusion System Describing Cell Interactions with a Medical Drug

In this paper, we study a nonlinear problem modeling the interaction between a chemotherapeutic drug and the normal, tumor, and immune cells. The macroscopic model for various cell densities and a medical drug is governed by a nonlinear reaction-diffusion system. We first derive some a priori estimates and then establish the global existence of a bounded solution for the nonlinear system. Finally, we study the long-time behavior of the solution for the model problem. These results will provide a theoretical foundation for scientists in the health and medical sciences to design an optimal drug dosage for cancer patients during a treatment when using a chemotherapeutic drug.