Optimising Antibiotic Usage to Treat Bacterial Infections

Abstract

The increase in antibiotic resistant bacteria poses a threat to the continued use of antibiotics to treat bacterial infections. The overuse and misuse of antibiotics has been identified as a significant driver in the emergence of resistance. Finding optimal treatment regimens is therefore critical in ensuring the prolonged effectiveness of these antibiotics. This study uses mathematical modelling to analyse the effect traditional treatment regimens have on the dynamics of a bacterial infection. Using a novel approach, a genetic algorithm, the study then identifies improved treatment regimens. Using a single antibiotic the genetic algorithm identifies regimens which minimise the amount of antibiotic used while maximising bacterial eradication. Although exact treatments are highly dependent on parameter values and initial bacterial load, a significant common trend is identified throughout the results. A treatment regimen consisting of a high initial dose followed by an extended tapering of doses is found to optimise the use of antibiotics. This consistently improves the success of eradicating infections, uses less antibiotic than traditional regimens and reduces the time to eradication. The use of genetic algorithms to optimise treatment regimens enables an extensive search of possible regimens, with previous regimens directing the search into regions of better performance.

Figure 1. Dynamics of the model over 30 days with antibiotic therapy administered at a daily dose of 23 μg/ml for the first 10 days.

(a) Stochastic simulations of the population dynamics of both susceptible (blue) and resistant (green) bacteria with the deterministic dynamics (bold) overlaid. 5000 simulations were run producing a success rate of eradicating the infection of 99.8% (95% CI: 99.6, 99.9). (b) Simulation of the concentration profile of antibiotic present within the system over the 30 day duration. The MIC lines indicate the concentration of antibiotic required to inhibit the growth of the respective bacterial strain, 16 μg/ml for susceptible bacteria and 32 μg/ml for resistant bacteria. A maximum antibiotic concentration of 60 μg/ml is observed on Day 10.

Figure 2. Concentration profiles for regimens D2, D5 and D8 from the dosage vectors identified by the GA with deterministic modelling.

(a) Treatment regimen D2 maintains an antibiotic concentration above the MIC of the resistant strain throughout the 6 day treatment. The maximum total concentration of antibiotic is 60 μg/ml. (b) D5 also maintains a concentration above the MIC for the resistant bacteria throughout the 6 day treatment reaching a maximum total concentration of 54 μg/ml on day 4. (c) The concentration of antibiotic throughout D8 increases above the MIC of the resistant bacteria initially but drops back below for the first two days. The concentration is then maintained above the resistant MIC for the remainder of the treatment, reaching a maximum concentration of 58 μg/ml on day 5.

Figure 3

Success rates for regimens S2 (pink), T3 (red) and S4 (blue) at varying values for parameters (a) a, (b) r, (c) g and (d) mic_R. Black dashed line shows original parameter values. As parameter values are altered to benefit the infection success rates for all three treatment regimens decrease. With the tapered regimens performing better than the traditional regimen. If parameter values are altered to disadvantage the infection the three regimens converge to a similar success rate.