Mean Exit Time and Escape Probability for a Tumor Growth System under Non-Gaussian Noise

TL;DR

This paper investigates how non-Gaussian alpha-stable Levy noise influences tumor growth dynamics by analyzing mean exit times and escape probabilities, revealing bifurcation phenomena through numerical simulations.

Contribution

It introduces a differential-integral equation with a fractional Laplacian to model tumor cell escape under non-Gaussian noise, highlighting bifurcation behaviors.

Findings

Bifurcation phenomena in mean exit time and escape probability as alpha varies

Numerical evaluation of tumor cell escape dynamics under non-Gaussian noise

Insights into tumor growth stability influenced by Levy noise

Abstract

Effects of non-Gaussian $\alpha-$stable L\'evy noise on the Gompertz tumor growth model are quantified by considering the mean exit time and escape probability of the cancer cell density from inside a safe or benign domain. The mean exit time and escape probability problems are formulated in a differential-integral equation with a fractional Laplacian operator. Numerical simulations are conducted to evaluate how the mean exit time and escape probability vary or bifurcates when $\alpha$ changes. Some bifurcation phenomena are observed and their impacts are discussed.