Dynamical transition of phenotypic states in breast cancer system with Lévy noise

Breast cancer cells exhibit three distinct phenotypes: basal, stem-like, and luminal states. These phenotypes are closely associated with the invasion and spread of breast cancer. As breast cancer has a high recurrence rate and rapid progression, it is critical to comprehend the mechanisms responsible for the transition between these states. This paper employs quantitative analysis to investigate the multiple phenotypic transition behaviors of the Lévy-noise-induced kinetic model of breast cancer using the first escape probability. The semi-analytical method of the first escape probability is constructed under Balayage–Dirichlet exterior boundary conditions. The results suggest that noise can trigger a transition from the basal state to the other two states, inducing breast cancer metastasis. Moreover, higher noise intensity promotes the transition from the basal state to the stem-like state, which can lead to tumor seeding. In addition, a larger amplitude with lower frequency of the jump increases the likelihood of transition from the basal state to the luminal state, indicating the formation of new tumors in distant organs that are difficult to treat. The validity and consistency of the proposed method can be verified by numerical simulations.