Asymmetric non-Gaussian effects in a tumor growth model with immunization

TL;DR

This paper investigates how asymmetric non-Gaussian noise influences tumor growth dynamics, revealing that such noise can potentially shorten tumor lifespan and increase extinction probability, offering insights into environmental effects on tumor evolution.

Contribution

It introduces the analysis of asymmetric non-Gaussian $ ext{Lévy}$ noise effects on tumor growth, highlighting their constructive role in tumor extinction dynamics, which is a novel perspective.

Findings

Asymmetric non-Gaussian noise can accelerate tumor extinction.

Adjusting noise parameters influences tumor lifetime and extinction probability.

Non-Gaussian noise effects differ significantly from Gaussian or symmetric noise.

Abstract

The dynamical evolution of a tumor growth model, under immune surveillance and subject to asymmetric non-Gaussian $\alpha$-stableL\'evy noise, is explored. The lifetime of a tumor staying in the range between the tumor-free state and the stable tumor state, and the likelihood of noise-inducing tumor extinction, are characterized by the mean exit time (also called mean residence time) and the escape probability, respectively. For various initial densities of tumor cells, the mean exit time and the escape probability are computed with different noise parameters. It is observed that unlike the Gaussian noise or symmetric non-Gaussian noise, the asymmetric non-Gaussian noise plays a constructive role in the tumor evolution in this simple model. By adjusting the noise parameters, the mean exit time can be shortened and the escape probability can be increased, simultaneously. This suggests that a tumor may be mitigated with higher probability in a shorter time, under certain external environmental stimuli.