Abstract

In this paper we review and at the same time 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 around 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 and the second order moments. We have studied 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 graphically represented using the second order Euler scheme and Maple 12 software.

Keywords: Lyapunov exponent, lyapunov function, stochastic models, stochastic stability, wiener process.