Abstract
A morbidostat is a bacteria culture device that maintains a nearly constant microbial population for the selection of drug-resistant mutants via a feedback algorithm. In this paper, the global dynamics of a microbial species undergoing sequential evolution are studied in detail to elucidate the operation of a morbidostat. The cultivation of the microbes is assumed to be under periodic dilution, and a simple threshold algorithm is used as feedback. We also prove the extinction and uniform persistence of all species with both forward and backward mutation in a sequential evolution scenario. Numerical simulations for the case of logistic growth and the Hill function for drug inhibition are also applied to verify our theoretical results. The theoretical framework elucidates the generic features of the operation of a morbidostat under drug-inhibitor-induced feedback and will provide a useful aid for the design of experiments.