A stochastic model for tumor growth with immunization

TL;DR

This paper introduces a stochastic model for tumor growth incorporating colored noise, immunization effects, and environmental influences, analyzing tumor extinction probabilities and the impact of various parameters.

Contribution

It presents a novel stochastic model that combines multiplicative and additive colored noise with cross-correlations to study tumor growth and immunization effects.

Findings

Immunization rate increases lead to a more pronounced maximum in the stationary distribution.

The mean-first passage time analysis reveals conditions favoring tumor extinction.

Cross-correlation strength significantly influences tumor dynamics and extinction likelihood.

Abstract

We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization, the birth rate is assumed to be stochastically changed due to biological motivated growth processes leading to a multiplicative internal noise. Moreover, the system is subjected to an external additive noise which mimics the influence of the environment of the tumor. The stationary probability distribution Ps is derived depending on the finite correlation time, the immunization rate and the strength of the crosscorrelation. Ps offers a maximum which becomes more pronounced for increasing immunization rate. The mean-first passage time is also calculated in order to find out under which conditions the tumor can suffer extinction. Its characteristics is again controlled by the degree of immunization and the strength of the cross-correlation. The behavior observed can be interpreted in terms of the three state model of a tumor population.