Abstract
In this paper we develop stochastic differential equation models for tumor population growth with immunization. We investigate especially the effect of a multiplicative noise on the progression of tumor evolution. Then, we perform a computational analysis in order to assess the behavior of the solution process. With this, we analyze the population extinction probability and the probability of persistence. In the case of persistence we analyze the behavior of the steady probability density and the evolution of its mean and variance. We further calculate the mean first passage time in order to describe the probability transitions between the extinction state and the state of the stable tumor. It is found that an increasing noise intensity rate enhances the probability of the extinction of the tumor.
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