Mathematical modeling of bacterial kinetics to predict the impact of antibiotic colonic exposure and treatment duration on the amount of resistant enterobacteria excreted

Abstract

Fecal excretion of antibiotics and resistant bacteria in the environment are major public health threats associated with extensive farming and modern medical care. Innovative strategies that can reduce the intestinal antibiotic concentrations during treatments are in development. However, the effect of lower exposure on the amount of resistant enterobacteria excreted has not been quantified, making it difficult to anticipate the impact of these strategies. Here, we introduce a bacterial kinetic model to capture the complex relationships between drug exposure, loss of susceptible enterobacteria and growth of resistant strains in the feces of piglets receiving placebo, 1.5 or 15 mg/kg/day ciprofloxacin, a fluoroquinolone, for 5 days. The model could well describe the kinetics of drug susceptible and resistant enterobacteria observed during treatment, and up to 22 days after treatment cessation. Next, the model was used to predict the expected amount of resistant enterobacteria excreted over an average piglet's lifetime (150 days) when varying drug exposure and treatment duration. For the clinically relevant dose of 15 mg/kg/day for 5 days, the total amount of resistant enterobacteria excreted was predicted to be reduced by 75% and 98% when reducing treatment duration to 3 and 1 day treatment, respectively. Alternatively, for a fixed 5-days treatment, the level of resistance excreted could be reduced by 18%, 33%, 57.5% and 97% if 3, 5, 10 and 30 times lower levels of colonic drug concentrations were achieved, respectively. This characterization on in vivo data of the dynamics of resistance to antibiotics in the colonic flora could provide new insights into the mechanism of dissemination of resistance and can be used to design strategies aiming to reduce it.

Figure 1. Model used for the kinetics of susceptible (S) and resistant (R) enterobacteria in presence of ciprofloxacin (C) in intestinal flora.

k_e is the elimination rate constant of intestinal ciprofloxacin concentrations; g _S and g _R are constant sources of susceptible and resistant bacteria respectively coming from outside; k _T is the rate constant of enterobacteria loss in absence of treatment; δ_max is the maximal killing rate of enterobacteria by ciprofloxacin; C _50S and C _50R are the ciprofloxacin concentrations at which 50% of the maximal killing effect occurs in susceptible and resistant enterobacteria respectively.

Figure 2. Experimental data from individual piglets (grey lines) and observed medians (black dots) versus medians predicted by the model (red lines) for fecal ciprofloxacin concentrations (first column), resistant (second column), total (third column) and susceptible enterobacteria (fourth column) in three treatment groups: A) placebo, B) ciprofloxacin 1.5 mg/kg/day, C) ciprofloxacin 15 mg/kg/day.

The red dotted lines represent the 10% and 90% quantiles of the estimated individual curves.

Figure 3. Resistant (first column), total (second column) and susceptible (third column) enterobacteria predicted for various fecal concentrations of ciprofloxacin C_ss: 0 µg/g (black), 0.9 µg/g (grey), 1.8 µg/g (violet), 2.9 µg/g (blue), 8.7 µg/g (green), 87 µg/g (red), for different treatment durations: A) 1 day, B) 3 days, C) 5 days; D) 10 days.

Figure 4. Predicted total amounts of resistant enterobacteria excreted for various levels of fecal ciprofloxacin concentrations and treatment duration.

Total amounts excreted and fecal ciprofloxacin concentrations are expressed as a relative reduction from the clinically relevant dose (15 mg/kg/day).