Optimal control strategies for disinfection of bacterial populations with persister and susceptible dynamics.

It is increasingly clear that bacteria manage to evade killing by antibiotics and antimicrobials in a variety of ways, including mutation, phenotypic variations, and formation of biofilms. With recent advances in understanding the dynamics of the tolerance mechanisms, there have been subsequent advances in understanding how to manipulate the bacterial environments to eradicate the bacteria. This study focuses on using mathematical techniques to find the optimal disinfection strategy to eliminate the bacteria while managing the load of antibiotic that is applied. In this model, the bacterial population is separated into those that are tolerant to the antibiotic and those that are susceptible to disinfection. There are transitions between the two populations whose rates depend on the chemical environment. Our results extend previous mathematical studies to include more realistic methods of applying the disinfectant. The goal is to provide experimentally testable predictions that have been lacking in previous mathematical studies. In particular, we provide the optimal disinfection protocol under a variety of assumptions within the model that can be used to validate or invalidate our simplifying assumptions and the experimental hypotheses that we used to develop the model. We find that constant dosing is not the optimal method for disinfection. Rather, cycling between application and withdrawal of the antibiotic yields the fastest killing of the bacteria.