Non-Gaussian dynamics of a tumor growth system with immunization

TL;DR

This study investigates how non-Gaussian α-stable Lévy noise influences tumor growth dynamics with immunization, revealing how noise parameters affect tumor extinction and stability, which can inform therapeutic strategies.

Contribution

It introduces a model incorporating non-Gaussian noise into tumor growth dynamics and analyzes how noise parameters impact tumor extinction and stability.

Findings

Noise parameters influence tumor extinction probability.

Different tumor stages respond differently to noise effects.

Results can guide effective tumor treatment strategies.

Abstract

This paper is devoted to exploring the effects of non-Gaussian fluctuations on dynamical evolution of a tumor growth model with immunization, subject to non-Gaussian {\alpha}-stable type L\'evy noise. The corresponding deterministic model has two meaningful states which represent the state of tumor extinction and the state of stable tumor, respectively. To characterize the lifetime for different initial densities of tumor cells staying in the domain between these two states and the likelihood of crossing this domain, the mean exit time and the escape probability are quantified by numerically solving differential integral equations with appropriate exterior boundary conditions. The relationships between the dynamical properties and the noise parameters are examined. It is found that in the different stages of tumor, the noise parameters have different influence on the lifetime and the likelihood inducing tumor extinction. These results are relevant for determining efficient therapeutic regimes to induce the extinction of tumor cells.