Evolutionary epidemiology models to predict the dynamics of antibiotic resistance

The evolution of resistance to antibiotics is a major public health problem and an example of rapid adaptation under natural selection by antibiotics. The dynamics of antibiotic resistance within and between hosts can be understood in the light of mathematical models that describe the epidemiology and evolution of the bacterial population. “Between‐host” models describe the spread of resistance in the host community, and in more specific settings such as hospitalized hosts (treated by antibiotics at a high rate), or farm animals. These models make predictions on the best strategies to limit the spread of resistance, such as reducing transmission or adapting the prescription of several antibiotics. Models can be fitted to epidemiological data in the context of intensive care units or hospitals to predict the impact of interventions on resistance. It has proven harder to explain the dynamics of resistance in the community at large, in particular because models often do not reproduce the observed coexistence of drug‐sensitive and drug‐resistant strains. “Within‐host” models describe the evolution of resistance within the treated host. They show that the risk of resistance emergence is maximal at an intermediate antibiotic dose, and some models successfully explain experimental data. New models that include the complex host population structure, the interaction between resistance‐determining loci and other loci, or integrating the within‐ and between‐host levels will allow better interpretation of epidemiological and genomic data from common pathogens and better prediction of the evolution of resistance.