Stochastic tumor growth system with two different kinds of time delay

Abstract

Abstract:The dynamical properties of a noise-driven tumor cell growth system are investigated when there exist two different kinds of time delays, in the deterministic and fluctuating forces, respectively. Using the approximation probability density approach, the delayed Fokker-Planck equation is obtained. The effects of two different time delays on the stationary probability distribution (SPD), the mean value and the mean passage time (MFPT) are discussed. It is found that the time delay τ 1 in the deterministic force can enhance tumor cell number, while the time delay In recent years, time-delayed stochastic processes have been the subject of increased interest in various fields. It was recently found that noise and delay can actually be an integral part of biological information processing [1,2]. Mainly, bistable systems with simultaneous noise and time delay have been investigated in detail. Ref.[3] founds noise induced resonance in delayed feedback systems. The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise has been studied analytically and numerically [4]. The noise-induced dynamics of a prototypical bistable system with delayed feedback have been studied theoretically and numerically [5]. Wu investigated the phe- * E-mail: cjwangbj@126.com nomenon of stochastic resonance in a bistable system with time-delayed feedback driven by non-Gaussian noise [6]. Biological systems subjected to simultaneous noise and time delay have especially attracted interest. For example, the effects of time delay on a mutualism system has been studied and it was found that the combination of the noise and the time delay completely suppresses population explosion [7]. The effects of time delay in competitive systems in the ecological field have been also studied. The results imply that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems [8]. The delay time also induces stochastic oscillations in gene regulation [9]. In many cases, the delay reflects transmission times related to the transport of matter, energy, and information through a system.The dynamical character of a tumor cell growth system subjected to a noise disturbance, which is described by 616 Unauthenticated Download Date | 5/11/18 6:53 AM

Gaussian and Lévy noises excited delayed tumor growth model: first-passage behavior and stochastic resonance

“…Many studies have shown that noise and time delay affect the transition between different steady states of tumor populations [19][20][21][22][23][24][25][26][27][28][29][40][41][42][43][44][45][46][47][48][49]. What sets this paper apart from previous research is that Gaussian white noise, Lévy noise and time delay are considered synergistically, and the results provide certain guidance for better study of the growth law of tumors, improve the treatment method of tumors, and enhance the level of tumor treatment.…”

“…Stochastic factor disturbance is also inevitable in the tumor growth model, and various noises are usually introduced for simulation. Researchers have looked into how various noises affect tumor growth in the past and have produced a number of significant findings [19][20][21][22][23][24][25][26][27][28][29]. Numerical simulations of the stationary probability density (SPD) of the delayed tumor-immune system in the presence of cross-correlated sine-Wiener noises were investigated by Guo et al [27].…”