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

Abstract

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.