Effect of tumor microenvironmental factors on the steady state of tumor growth with non-zero correlation time

Abstract

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.

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

“…In the study of tumor cell growth, mathematical model equations that closely captures the general features of tumor growth are considered in literature, and logistic equation is the most widely used deterministic model for theoretical study [13]. Moreover, real tumor growth model should be subject to influences from internal and external random environmental factors such as effects from external therapeutic control [14][15][16], and from internal tumor microenvironmental processes [17][18][19].…”