Bacterial persistence: Mathematical modeling and optimal treatment strategy

Bacterial persistence is an epigenetic phenomenon in which some bacteria cells become immune to antibiotic treatment without undergoing genetic mutation. In this paper, we develop a population dynamic model that captures both short term and long term persistence in bacteria. We subsequently pose the problem of designing an optimal treatment strategy, in terms of minimizing the number of persister cells that transition into long term dormancy. We find that the infinite time horizon optimal control strategy is not unique, and it can be expressed as a feedback law using the information about the population sizes of normal and persister cells. We also show the existence of a theoretical lower bound for the optimal cost value.