Mean first-passage time for a stochastic tumor growth model with two different time delays

In this paper, the mean first-passage time (MFPT) of a stochastic tumor growth model driven by correlated white noises with two different time delays is investigated. The small time delay approximation is utilized to obtain the generalized potential function and the MFPT, and a detailed analysis is conducted on how time delays and noise parameters affect the generalized potential function and the MFPT, respectively. We further validate the effectiveness of the theoretical results using the fourth-order Runge–Kutta algorithm. The findings indicate that (1) when the intensity of multiplicative noise is higher and the intensity of additive noise is lower, there is a greater likelihood of tumor cells dying off, which promotes the healing of the system; (2) an increase in the correlation strength between multiplicative noise and additive noise promotes the carcinogenesis of tumor cells and accelerates the deterioration of the system; (3) increasing the time delay in the deterministic force and decreasing the time delay in the stochastic force lead to a higher likelihood of tumor cell extinction. Furthermore, the phenomenon of noise enhanced stability (NES) is found.