Cross-correlated sine-Wiener noises-induced transitions in a tumor growth system

Abstract

Cross-correlated sine-Wiener (CCSW) noises-induced transitions in a stochastic tumor growth dynamical system are studied. Utilizing Fox’s approach and Hänggi ansatz, the role of CCSW noises on dynamical systems is equivalently transformed into that of multiplicative Gaussian white noise, effectively solving the dynamics puzzles caused by CCSW noises and facilitating the intractable theoretical investigation related to CCSW noises. The impacts of CCSW noises on transitions between the high-population (undesirable) basin B1 and low-population (desirable) basin B2, available to describe the process of tumor elimination and recurrence, are examined theoretically and numerically from the perspective of basin stability through the first escape probability (FEP) and mean first exit time (MFET). Lower FEP or longer MFET characterizing stronger stability reflects a lower likelihood of transitions. Four stability indexes, δE, δSBA, δR, and δSBA∗, are considered to fully explore the role of CCSW noises on transitions between B1 and B2 to reveal its contribution during different tumor treatment stages. We discover that (i) the CCSW noise intensities exert a dual effect on transitions: for λ≤0 (cross-correlation strength), enhanced noise intensities lead to smaller δE (/δSBA) or larger δR (or smaller δSBA∗), acting to weaken the undesirable or desirable basin stability and favor transitions; for λ>0, critical noise intensities that maximize δE (/δSBA) or minimize δR (or maximize δSBA∗) exist, indicating that noise-enhanced stability occurs, which can be reinforced by enhancing λ. (ii) Increasing the correlation time τ leads to weaker stability and higher transition probability, while λ acts oppositely in inducing transitions. Therefore, to achieve better tumor eradication efficacy, destabilizing the undesirable basin B1 by enhancing the negatively correlated SW noise intensities and increasing τ is urgent. During the stage of suppressing tumor recurrence, the unsafe parameter domain that causes a larger δR, implying a high risk of re-entry into B1, should be eschewed. Instead, the positively correlated critical noise intensities with a larger λ and smaller τ for stabilizing the desirable basin B2 are preferable.