Abstract
In this paper, a competition model between tumor cells and immune system with random switching environment is proposed and investigated. The stochastic switching environment is assumed to be telegraph noise expressed as multi-state Markov chain. The theoretical threshold for extinction and persistence of tumor cells are obtained. Besides, stochastic simulations are performed to substantiate and interpret the conclusions. It is found that stochastic switching environment plays an important part in the process of tumor evolution. The simple model proposed in our paper is conducive to understand the theoretical mechanism between tumor cells and immune system under random environment.
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