# On the role of cancer cells' diffusion in the tumor growth paradox

## TL;DR

This paper reviews a mathematical model explaining the tumor growth paradox, showing that cancer cell diffusion and boundary conditions can lead to increased tumor growth despite treatment.

## Contribution

It demonstrates that incorporating diffusion effects and boundary conditions in the model reproduces the tumor growth paradox observed in incomplete cancer treatments.

## Key findings

- Diffusion effects contribute to tumor growth paradox.
- Neumann boundary conditions are crucial in the model.
- The paradox persists under realistic diffusion assumptions.

## Abstract

In this contribution, the non-local, integro-partial differential system of equations proposed by Hillen et al. (Bull. Math. Biol. 75, 2013, no.1, 161-184) to account for the the tumor growth paradox (or the observation that some incomplete cancer treatments may enhance tumor growth) is reviewed. It is shown that when cancer cells' diffusion effects and Neumann boundary conditions are taken into consideration, the same paradoxical tumor growth emerges.