Review of Stochastic Stability and Analysis Tumor-Immune Systems
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.
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