A stochastic analysis of the interplay between antibiotic dose, mode of action, and bacterial competition in the evolution of antibiotic resistance

Author summaryAntibiotic treatment creates a beneficial environment for the evolution of antibiotic-resistant bacterial strains. The dosage of the antibiotic drug during treatment plays an important role during this process. Here, we derive analytical predictions for the survival probability of a resistant subpopulation until the end of treatment with either a biostatic, i.e. growth-inhibiting, or a biocidal, i.e. death-promoting, drug. Importantly, we obtain a prediction for the antibiotic concentration that maximizes this survival probability. Additionally, we also compute the size of the resistant subpopulation at the end of treatment and its carriage time after treatment until it gets outcompeted by an antibiotic-sensitive strain. This post-treatment phase is relevant only for commensal bacteria. We find that treatment with a biocidal drug, compared to a biostatic drug, increases the risk of resistance evolution, results in a larger resistant subpopulation size at the end of treatment and prolongs the carriage time, and therefore shedding, of the resistant strain. Our analytical predictions can be tested experimentally and link the within-host and the population scale of antibiotic resistance dynamics. The use of an antibiotic may lead to the emergence and spread of bacterial strains resistant to this antibiotic. Experimental and theoretical studies have investigated the drug dose that minimizes the risk of resistance evolution over the course of treatment of an individual, showing that the optimal dose will either be the highest or the lowest drug concentration possible to administer; however, no analytical results exist that help decide between these two extremes. To address this gap, we develop a stochastic mathematical model of bacterial dynamics under antibiotic treatment. We explore various scenarios of density regulation (bacterial density affects cell birth or death rates), and antibiotic modes of action (biostatic or biocidal). We derive analytical results for the survival probability of the resistant subpopulation until the end of treatment, the size of the resistant subpopulation at the end of treatment, the carriage time of the resistant subpopulation until it is replaced by a sensitive one after treatment, and we verify these results with stochastic simulations. We find that the scenario of density regulation and the drug mode of action are important determinants of the survival of a resistant subpopulation. Resistant cells survive best when bacterial competition reduces cell birth and under biocidal antibiotics. Compared to an analogous deterministic model, the population size reached by the resistant type is larger and carriage time is slightly reduced by stochastic loss of resistant cells. Moreover, we obtain an analytical prediction of the antibiotic concentration that maximizes the survival of resistant cells, which may help to decide which drug dosage (not) to administer. Our results are amenable to experimental tests and help link the within and between host scales in epidemiological models.