Average break-even concentration in a simple chemostat model with telegraph noise

In this paper, we aim to investigate the effect of telegraph noise on the continuous culture of microorganism in a chemostat. With the help of a finite-state Markov chain, we first construct a regime-switching chemostat model and then establish conditions for extinction and persistence of the microorganism. It is shown that the particular outcome of the chemostat is completely determined by a defined average break-even concentration λA: The microorganism becomes extinct in the chemostat when λA>S0, the input substrate concentration; it will persist when λA