Abstract
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.
Highlights
The evolution of resistance to antibiotics in bacterial pathogens is an example of rapid evolution in action
Coexis‐ tence between the two strains is possible in a narrow window of treatment rates, because the treated hosts form a niche in which the resistant strain can multiply
When the treatment rate exceeds the upper value of this narrow window, resistance fixes in the popula‐ tion. This model was fitted to data to quantify the impact of a change in antibiotic consumption on the dynamics of resistance (Austin, Kristinsson, & Anderson, 1999)
Summary
The evolution of resistance to antibiotics in bacterial pathogens is an example of rapid evolution in action. Models of resistance evolution need to consider various heterogeneities in the host population, different levels of selection (within and between hosts), and the interplay between the demography of the pathogen (prevalence of the infection at the population level; demography within the host) and the evolution of resistance These processes generate complex and interesting dy‐ namics described in this review. Models of antibiotic resistance evolution have flourished, often building on classical differential equation compartmental epi‐ demiological models (Kermack & McKendrick, 1927) popularized by Anderson and May (1991) These models describe the evolution of a bacterial population composed of a sensitive (“S”) and a resistant (“R”) strain colonizing a host population (Box 1). The evolution and reversion of resistance are both extremely rapid, and
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