Steady state analysis for the effect of tumor microenvironmental factors on tumor growth dynamics driven by correlated noises

The steady state analysis for the effect of non-immunogenic tumor microenvironmental factors modeled by correlated additive and multi- plicative noises with zero correlation time is investigated. The underlying transition probability for the stochastic model equation satisfies the Markovian Fokker-Planck equation, and the steady state distribution ρst(x) for the tumor growth system is derived. Based on the numerical computation, we find that the effect of non-immunogenic microenviron-mental factors within the tumor site with strength θ have a diffusive effect on the steady state distribution ρst(x), and the tumor response to the surrounding non-immunogenic microenvironmental factors effects with strength D inhibits growth on both the steady state distribution ρst (x) and the mean〈x〉st of the tumor population. The result also indicates that the stronger the correlation strength φ, the more the tumor responded to the surrounding non-immunogenic microenviron- mental factors effect.

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