The COVID-19 pandemic has renewed the demand for quantitative models capable of describing the spread of respiratory pathogens in structured human populations, and of supporting public-health decisions on non-pharmaceutical interventions in real time. The accuracy of these models depends on how faithfully they represent the contacts through which the pathogen is transmitted. The simplest representation, introduced by Kermack and McKendrick almost a century ago , assumes that every individual mixes homogeneously with every other and reduces the dynamics of an outbreak to a small system of ordinary differential equations on population-level compartments. This assumption is plainly violated in real populations, where contact patterns depend strongly on the age of the individuals involved, on the setting in which they meet, and on the regularity with which they encounter each other.