Stochastic model for tumor growth with immunization.

We analyze a stochastic model for tumor cell growth with both multiplicative and additive colored noises as well as nonzero 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 P_{s} is derived depending on the finite correlation time, the immunization rate, and the strength of the cross correlation. P_{s} 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 are again controlled by the degree of immunization and the strength of the cross correlation. The behavior observed can be interpreted in terms of a biological model of tumor evolution.