Over the past few decades, the emergence of multidrug resistance (MDR) to antibiotics in bacteria has led to major difficulties in the management of infected patients. At present, there is a serious lack of development of new antibacterial agents. Mathematical models are one approach to understand how antibiotic usage patterns may be optimized. However, the classical approach to modeling the emergence of MDR relies on the simplifying assumption that resistance is acquired at a constant rate. In their model, Obolski and Hadany introduce the notion of horizontal gene transfer and stress-induced mutation, with antibiotics constituting an environmental stressor of particular relevance. Finally, from this complex mathematical model, the authors propose predictions for minimizing MDR in bacteria depending on strategies of antibiotic treatment.

In their rationale, Obolski and Hadany highlighted the importance of three different strategies (cycling, mixing and combining) of antibiotic prescribing to minimize the emergence of MDR. In the cycling regime, antibiotic treatment is the same for all patients at a given time and the treatment is periodically switched. In the mixing strategy, each patient receives a randomly selected drug. Combining involves administering several antibiotic treatments to each patient. The authors noted the ability of each strategy to prevent the risk of emergence of MDR, indicating that more antibiotics were used in combining than in mixing or cycling. They emphasize that the classical approach to modeling the emergence of MDR relies on the simplifying assumption that resistance is acquired at a constant rate, ignoring recent data on the effect of environmental stress on mechanisms of acquired resistance. This erroneous assumption could be the cause of frequent reservations in the conclusions of these models. Moreover, the actual effect of a single intervention in a complex situation is often difficult to grasp [3]. The originality in the model used by Obolski and Hadany is to introduce the notion of horizontal gene transfer (HGT) and stress-induced mutation (SIM), antibiotics constituting an environmental stressor of particular relevance. The authors justify this hypothesis by showing examples of stress-induced HGT and SIM for various microorganisms that may be encountered in community-acquired infections (Streptococcus pneumoniae, Escherichia coli), nosocomial (Pseudomonas aeruginosa, E. coli) or epidemic infections (Vibrio cholerae). The model is used, but adapted to integrate the concepts of stress-induced HGT and SIM [4]. The authors also introduce some constraints in the model: (i) the bacterial pathogens are assumed to accompany other ailments and not be the main reason for hospitalization, (ii) since the bacterial infection is not the main reason of hospitalization patients leave the hospital or die at a rate proportional to their frequency, (iii) hospital occupancy is kept constant, (iv) there are no double-resistant bacteria in the hospital initially, and that their frequency in the general population is negligible. Concerning the SIM, they also took into consideration modeling the relative persistence of antibiotic resistance when there is no direct antibiotic use. The introduction of different level assumptions (antibiotic resistance persistence and stress-induced mutation) has had different consequences in terms of the proportion of infected patients and emergence of resistance. Indeed, the latter two parameters may vary either in the same direction or in the opposite direction in functions of the hypotheses. Another mechanism of acquisition of antibiotic resistance studied in this model was HGT. The latter was studied in defining an encounter rate between bacteria. The authors also considered situations in which the bacteria were or were not under antibiotic stress. They developed the notion of time required for the cellular mechanisms to induce or repress HGT. They defined an extreme situation where the HGT rates of bacteria transmitted from patient A to patient B depend only on the stress of the bacteria experienced while residing in patient A. Thus, assessing the effects of different antibiotic regimens with respect to the encounter rates between bacteria is complex.

The present model has shown that combining was slightly more efficient than mixing and cycling with regard to minimizing infection. Regarding double resistance emergence, both mixing and cycling were more efficient than combining when variation is stress induced.

AS (MD, PhD) is head of the Infectious Diseases Department of the University Hospital of Nîmes. He is currently affiliated with, and conducting research at, the National Institute of Health and Medical Research, U1047, Faculty of Medicine, Montpellier 1 University, Montpellier, France.

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