The effect of enrofloxacin on enteric Escherichia coli: Fitting a mathematical model to in vivo data

Abstract

Antimicrobial drugs administered systemically may cause the emergence and dissemination of antimicrobial resistance among enteric bacteria. To develop logical, research-based recommendations for food animal veterinarians, we must understand how to maximize antimicrobial drug efficacy while minimizing risk of antimicrobial resistance. Our objective is to evaluate the effect of two approved dosing regimens of enrofloxacin (a single high dose or three low doses) on Escherichia coli in cattle. We look specifically at bacteria above and below the epidemiological cutoff (ECOFF), above which the bacteria are likely to have an acquired or mutational resistance to enrofloxacin. We developed a differential equation model for the antimicrobial drug concentrations in plasma and colon, and bacteria populations in the feces. The model was fit to animal data of drug concentrations in the plasma and colon obtained using ultrafiltration probes. Fecal E. coli counts and minimum inhibitory concentrations were measured for the week after receiving the antimicrobial drug. We predict that the antimicrobial susceptibility of the bacteria above the ECOFF pre-treatment strongly affects the composition of the bacteria following treatment. Faster removal of the antimicrobial drugs from the colon throughout the study leads to improved clearance of bacteria above the ECOFF in the low dose regimen. If we assume a fitness cost is associated with bacteria above the ECOFF, the increased fitness costs leads to reduction of bacteria above the ECOFF in the low dose study. These results suggest the initial E. coli susceptibility is a strong indicator of how steers respond to antimicrobial drug treatment.

Fig 1. ODE schematic.

Schematic of the mathematical model for enrofloxacin and ciprofloxacin concentrations throughout the gastrointestinal tract (GIT) of the steer and the effects on the E. coli population. The compartments S, P, and C are antimicrobial concentration in the steer while the compartments E and R describe the bacteria population in the feces.

Fig 2. High dose steer dynamics.

Prediction of the high dose treatment group. Estimation of the concentration of antimicrobial drugs in the plasma, P, colon, C and estimation of the amount of the total E. coli and E. coli above the ECOFF in the feces. Each steer is represented by the same color for model predictions (lines) and corresponding data (dots). The median population estimate for each compartment is the black dashed line.

Fig 3. Low dose steer dynamics.

Prediction of the low dose treatment group. Estimation of the concentration of antimicrobial drugs in the plasma, P, colon, C and estimation of the amount of the total E. coli and E. coli above the ECOFF in the feces. Each steer is represented by the same color for model predictions (lines) and corresponding data (dots). The median population estimate for each compartment is the black dashed line.

Fig 4. High dose distributions.

Predicted distribution of our model for the antimicrobial drugs concentration throughout the GIT of the steer during the high dosing regimen. The top left panel is the plasma, the bottom left is the colon, top right the total E. coli population and bottom right is E. coli above the ECOFF. In each panel, the dark line represents the median, and the darkest blue region has a 50% likelihood, whereas the lighter colors are less likely to occur.

Fig 5. Low dose distributions.

Predicted distribution of our model for the antimicrobial drug concentration throughout the GIT of the steer during the low dosing regimen. The top left panel is the plasma, the bottom left is the colon, top right is the total E. coli population and bottom right is the amount of E. coli above the ECOFF. In each panel, the dark line is the median, and the darkest blue region has a 50% likelihood, whereas the lighter colors are less likely to occur.

Fig 6. High dose sensitivity analysis.

Sobol sensitivity analysis results of the high dose regime. The left panel is a histogram of the output variable of the sensitivity analysis, the area under the curve of the bacteria above the ECOFF, R. The right panel is the sensitivity index for each parameters. The first order effects measures varying the parameter alone but averaged across all of the other variations while the total effect measures the effect of varying the parameters including variance caused by the parameters interactions.

Fig 7. Low dose sensitivity analysis.

Sobol sensitivity analysis results of the low dose regime. The left panel is a histogram of the output variable of the sensitivity analysis, the area under the curve of the bacteria above the ECOFF, R. The right panel is the sensitivity index for each parameters. The first order effects measures varying the parameter alone but averaged across all of the other variations while the total effect measures the effect of varying the parameters including variance caused by the parameters interactions.

Fig 8. Variations in C_s50.

Simulation of variations of C_s50 and the effects on the high (top row) and low (bottom row) dose model (1). In the simulation C_s50 is varied from the initial estimate of 6.05 or 2.02 (black line) for the high and low dose model, respectively. We vary C_s50 with incremental values of 7 (red line), 6 (blue line), 5 (green line), 4 (purple line), 3 (orange line), 2 (pink line) and 1 (grey line).

Fig 9. Variations in η.

Varying η, the elimination of the drug from the colon, to understand the changes that occur in sick or non-normal steers in the low and high dose study. The black line represents the average steer simulation, the red line is slow movement (η = 0.01) and the blue line is rapid movement (η = 0.8).

Fig 10. Varying initial bacteria.

We shift only the initial condition r₀ from 0 to the total amount of E. coli in each treatment and investigate how this effects the fraction of R/E, or the proportion of E. coli about ECOFF.

Fig 11. Varying fitness cost.

Varying c, the fitness cost, to understand the effect on the ratio of R/E at 200 hours for each dosing regimen. Each line represents a different amounts of r₀.