The analysis of stochastic stability of stochastic models that describe tumor-immune systems

TL;DR

This paper investigates the stochastic stability of tumor-immune system models using Lyapunov methods and numerical simulations, highlighting the stabilizing role of noise in these biological systems.

Contribution

It introduces stochastic models for tumor-immune interactions and analyzes their stability using Lyapunov functions and exponents, providing new insights into their dynamic behavior.

Findings

Stochastic noise has a stabilizing effect on tumor-immune models.

Lyapunov functions confirm stochastic stability of the models.

Numerical simulations support theoretical stability results.

Abstract

In this paper we investigate some stochastic models for tumor-immune systems. To describe these models, we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability in the equilibrium points, by constructing the Lyapunov exponent, depending on the parameters that describe the model. Stochastic stability was also proved by constructing a Lyapunov function. We have studied and and analyzed a Kuznetsov-Taylor like stochastic model and a Bell stochastic model for tumor-immune systems. These stochastic models are studied from stability point of view and they were represented using the second Euler scheme and Maple 12 software.