Stochastic tumor growth system with two different kinds of time delay

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 τ₁ in the deterministic force can enhance tumor cell number, while the time delay τ₂ in the fluctuating force can induce a decrease in tumor cell numbers. On the other hand, while τ₁ can hold back the extinction of tumor cells, τ₂ can speed up their extinction.