Tumor state transitions driven by Gaussian and non-Gaussian noises

Abstract

Tumor state transitions between the excited (high-concentration) and nonexcited (low-concentration) basins under the Gaussian white noise and non-Gaussian colored noise are investigated via the most probable steady states (MPSS) and the first escape probability (FEP)-based stochastic basin of attraction (SBA), respectively. Reducing the non-Gaussian colored noise and then utilizing the unified colored noise approximation (UCNA), the Markov system is derived. The extremal controlling equation of stationary probability density function (SPDF) is derived to analyze the impacts of noise on transitions in terms of MPSS. The existence of the ‘color’ of the non-Gaussian colored noise induces the reappearance of the uncorrelated additive white noise parameter that had vanished from the extremal controlling equation, completely reversing the inability of the uncorrelated additive Gaussian white noise to operate on transitions. The FEP-dependent SBA characterizing the excited basin stability is performed to further analyze the role of noise on the likelihood of escaping to the nonexcited state. Results show that the cross-correlated noises play a dual role in regulating SBA. The increased SBA indicating more difficulty to escape to the nonexcited state reflects a worse therapeutic effect. Therefore, enhancing the negatively correlated noise intensities and augmenting the non-Gaussian noise correlation time is essential for destabilizing the excited basin and achieving optimal therapeutic efficacy.