# Tumor growth, $R$-positivity, Multitype branching and Quasistationarity

## TL;DR

This paper investigates the mathematical properties of tumor growth models using Markov processes and positive matrices, establishing conditions for their long-term behavior and applying these to understand tumor size dynamics.

## Contribution

It introduces new conditions for R-positivity in Markov processes and positive matrices, and applies these to analyze tumor size asymptotics in supercritical regimes.

## Key findings

- Conditions for R-positivity established
- Asymptotic behavior of tumor sizes derived
- Application to supercritical tumor growth models

## Abstract

Motivated by tumor growth models we establish conditions for the $R-$positivity of Markov processes and positive matrices. We then apply them to obtain the asymptotic behavior of the tumors sizes in the supercritical regime.