Optimal antimicrobial dosing combinations when drug-resistance mutation rates differ

Given the ongoing antimicrobial resistance crisis, it is imperative to develop dosing regimens optimised to avoid the evolution of resistance. The rate at which bacteria acquire resistance-conferring mutations to different antimicrobial drugs spans multiple orders of magnitude. By using a mathematical model and computer simulations, we show that knowledge of relative mutation rates can meaningfully inform the optimal combination of two drugs in a treatment regimen. We demonstrate that under plausible assumptions there is a linear relationship in log-log space between the drug A:drug B dose ratio that maximises the chance of treatment success and the ratio of their mutation rates. This power law relationship holds for bacteriostatic and bactericidal drugs. If borne out empirically, these findings suggest there might be significant room to further optimise antimicrobial dosing strategies.