Non-Gaussian dynamics of a tumor growth system with immunization

Abstract

This paper is devoted to exploring the effects of non-Gaussianfluctuations on dynamical evolution of a tumor growth model withimmunization, subject to non-Gaussian $\alpha$-stable type Lévynoise. The corresponding deterministic model has two meaningfulstates which represent the state of tumor extinction and the stateof stable tumor, respectively. To characterize the time fordifferent initial densities of tumor cells staying in the domainbetween these two states and the likelihood of crossing this domain,the mean exit time and the escape probability are quantified bynumerically solving differential-integral equations with appropriateexterior boundary conditions. The relationships between thedynamical properties and the noise parameters are examined. It isfound that in the different stages of tumor, the noise parametershave different influences on the time and the likelihood inducingtumor extinction. These results are relevant for determiningefficient therapeutic regimes to induce the extinction of tumorcells.