Persistence criteria for a chemostat with variable nutrient input and variable washout with delayed response in growth

We study a general single-species chemostat model with non-autonomous input and washout, and a discrete-time delay between consumption of the nutrient and growth. The goal of this article is to provide sufficient and necessary conditions for persistence. The persistence criteria obtained here extend previous works done for the autonomous model with delay and for the non-autonomous model without delay. Furthermore, in the particular case of periodic nutrient input and the same periodic washout with delayed response in growth, the persistence criteria can be expressed in terms of the average of the involved functions. We remark in no case we need to impose any restrictions on the size of the delay. •We provide sufficient and necessary conditions for persistence.•The criteria obtanied extend previous works done in the autonomous model with delay.•They also extend previous works on the the non-autonomous model without delay.•In the periodic case we provide specific criteria.•The results do not require conditions on the size of the delay.