Stochastic dynamics of tumor growth model under switching

In this paper, a single-variable tumor growth model perturbed by both white noise and switching is developed and analyzed. The switching is modeled by telegraph noise expressed as multi-state Markov chain. First, threshold conditions of weak persistence and extinction of tumor cells are deduced strictly. Second, we obtain the sufficient condition of stochastic permanence for tumor. Besides, several numerical simulations are performed to validate the above theoretical results. In fact, our works present that switching plays an extremely significant role in the tumor extinction, and our constructed model is conducive to study the complex tumor growth mechanism from a new perspective under random environment.