Developing feasible strategies and setting realistic targets for disease prevention and control depends on representative models, whether conceptual, experimental, logistical or mathematical. Mathematical modelling was established in infectious diseases over a century ago, with the seminal works of Ross and others. Propelled by the discovery of etiological agents for infectious diseases, and Koch's postulates, models have focused on the complexities of pathogen transmission and evolution to understand and predict disease trends in greater depth. This has led to their adoption by policy makers; however, as model-informed policies are being implemented, the inaccuracies of some predictions are increasingly apparent, most notably their tendency to overestimate the impact of control interventions. Here, we discuss how these discrepancies could be explained by methodological limitations in capturing the effects of heterogeneity in real-world systems. We suggest that improvements could derive from theory developed in demography to study variation in life-expectancy and ageing. Using simulations, we illustrate the problem and its impact, and formulate a pragmatic way forward.