The effect of non-immunogenic tumor microenvironmental factors on the steady state tumor growth dynamics modeled by multiplicative colored noise is investigated. Using the Novikov theorem and Fox approach, an approximate Fokker-Planck equation for the non-Markovian stochastic model is obtained and analytic expression for the steady state distribution P st (x) is derived. We find that the strength of the tumor response to the microenvironmental factors effect θ reduces the value of the steady state distribution P st (x) of tumor growth at weak correlation time τ which is an inhibitive effect, and at strong correlation time the inhibitive effect is suppressed and instead the value of the steady state distribution is increased which corresponds to growth enhancement. The result indicated that the growth effect exerted by the non-immunogenic tumor microenvironmental factors on tumor growth depend on the correlation time strength τ of the tumor response.

The effect of non-immunogenic tumor microenvironmental factors on tumor growth dynamics modeled by correlated additive and multiplicative colored noises is investigated. Using the Novikov theorem, Fox approach and Ansatz of Hanggi, an approximate Fokker-Planck equation for the system is obtained and analytic expression for the steady state distribution Pst(x) is derived. Based on the numerical results, we find that fluctuations of microenvironmental factors within the tumor site with parameter θ have a diffusive effect on the tumor growth dynamics, and the tumor response to the microenvironmental factors with parameter α inhibits growth at weak correlation time τ. Moreover, at increasing correlation time τ the inhibitive effect of tumor response α is suppressed and instead a systematic growth promotion is noticed. The result also reveals that the strength of the correlation time τ has a strong influence on the growth effects exerted by the non-immunogenic component of tumor microenvironment on tumor growth.

The steady state analysis for the effect of non-immunogenic tumor microenvironmental factors modeled by correlated additive and multiplicative 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 ρ st (x) for the tumor growth system is derived. Based on the numerical computation, we find that the effect of non-immunogenic microenvironmental factors within the tumor site with strength θ have a diffusive effect on the steady state distribution ρ st (x), and the tumor response to the surrounding non-immunogenic microenvironmental factors effects with strength D inhibits growth on both the steady state distribution ρ st (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 microenvironmental factors effect.

The steady state properties for the effect of non-immunogenic microenvironmental factors on tumor growth dynamics in the presence of immune response is investigated. The corresponding Fokker-Planck equation to the Langevin model equation interpreted in the sense of Stratonovich is used to derive the steady state distribution ρst (x) and the mean 〈x 〉st of the tumor growth system. We find that the correlation strength ϕ stimulates the effect of the non-immunogenic microenvironmental factors σ on the tumor growth dynamics, and the tumor response M to the non-immunogenic microenvironmental factors within the tumor site may inhibits tumor growth, but not sufficient enough to cause extinction. Moreover, the result also indicates that the stronger the immune response λ the more the tumor population disappears.