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The paper considers a chemostat model describing an activated sludge processin wastewater treatment. The model is assumed to be subject to environmentnoise in terms of both white noise and color noise. The paper fullycharacterizes the asymptotic behavior of the model that is a hybrid switchingdiffusion. We show that the long-term properties of the system can beclassified using a value $\lambda$. More precisely, if $\lambda\leq 0$, thebacteria in the sewage will die out, which means that the process does notoperate. If $\lambda>0$, the system has an invariant probability measure towhich the transition probability of the solution process convergesexponentially fast. One of the distinctive contributions of this paper is thatthe critical case $\lambda=0$ is considered. Numerical examples are given toillustrate our results.

General Nonlinear Stochastic Systems Motivated by Chemostat Models:  Complete Characterization of Long-Time Behavior, Optimal Controls, and  Applications to Wastewater Treatment