Effect of tumor microenvironmental factors on tumor growth dynamics modeled by correlated colored noises with colored cross-correlation

• Effect of non-immunogenic microenvironmental factors on tumor growth is investigated.
• The steady state distribution for the tumor growth system is derived.
• The non-immunogenic microenvironmental factors effects inhibits tumor growth.
• The strength of the correlation time ττ exerts growth effect on the tumor growth system.

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)Pst(x) is derived. Based on the numerical results, we find that fluctuations of microenvironmental factors within the tumor site with parameter θθ have a diffusive effect on the tumor growth dynamics, and the tumor response to the microenvironmental factors with parameter αα inhibits growth at weak correlation time ττ. Moreover, at increasing correlation time ττ the inhibitive effect of tumor response αα is suppressed and instead a systematic growth promotion is noticed. The result also reveals that the strength of the correlation time ττ has a strong influence on the growth effects exerted by the non-immunogenic component of tumor microenvironment on tumor growth.