Transition in a delayed tumor growth model with non-Gaussian colored noise

Transition in a delayed tumor growth model subjected to non-Gaussian colored noise is investigated. The lifetime of residing in the excited region, and the likelihood of first escaping to the nonexcited region, are characterized via mean first exit time (MFET) and first escape probability (FEP). A shorter MFET or higher FEP, signifying a higher probability of transition and weaker basin stability, favors tumor control in terms of treatment time and cure rate. Stochastic basin of attraction (SBA), introduced for further understanding of basin stability, allows to depict the effectiveness of treatments. Additionally, the average level of MFET and FEP (i.e., AMFET and AFEP) is utilized to examine the whole escape behaviors. The results reveal that (i) enhancing the non-Gaussian noise fluctuation significantly reduces MFET, while time delay modulates MFET in a double-faced manner. Consequently, AMFET acts a non-monotonic dependence on delay under different noise intensities. Comprehensive analysis suggests that a stronger fluctuation combined with a smaller delay is suitable for inducing transition within a shorter residence time. (ii) The larger noise intensity and deviation parameter raise FEP and lessen the size of SBA, thus facilitating transition and weakening basin stability, which means better treatment effectiveness. However, time delay behaves oppositely, suggesting that treatments with excessive delay are less effective and should be avoided in clinical practice. Therefore, to achieve better therapeutic effects in a short treatment time, reinforcing the fluctuation of immune rate caused by microenvironmental factors and shortening the reaction time of human bodies to treatments are recommended.

Automated summary

This study investigates the transition in a delayed tumor growth model under the influence of non-Gaussian colored noise. The mean first exit time (MFET) and first escape probability (FEP) are used to characterize the lifetime of residing in the excited region and the likelihood of first escaping to the nonexcited region. The results show that a shorter MFET or higher FEP favors tumor control and weaker basin stability, indicating better treatment effectiveness. Furthermore, the analysis suggests that enhancing non-Gaussian noise fluctuation and reducing time delay can lead to faster transitions and improved therapeutic outcomes.