# An analysis of a mathematical model describing the growth of a tumor treated with chemotherapy

## TL;DR

This paper analyzes a mathematical model combining ODEs and PDEs to describe tumor and normal cell growth under localized chemotherapy, providing theoretical results and numerical simulations.

## Contribution

It introduces a novel mixed ODE-PDE model for tumor growth with localized drug delivery, including existence, uniqueness, and simulation results.

## Key findings

- Model exhibits different behaviors depending on parameters.
- Existence and uniqueness of solutions are established.
- Numerical simulations illustrate tumor response to therapy.

## Abstract

We present a mathematical analysis of a mixed ODE-PDE model describing the spatial distribution and temporal evolution of tumor and normal cells within a tissue subject to the effects of a chemotherapeutic drug. The model assumes that the influx of chemotherapy is restricted to a limited region of the tissue, mimicking a blood vessel passing transversely. We provide results on the existence and uniqueness of the model solution and numerical simulations illustrating different model behaviors.