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Measles epidemics in human populations exhibit what is perhaps the best empirically characterized, and certainly the most studied, stochastic persistence threshold in population biology. A critical community size (CCS) of around 250 000–500 000 separates populations where measles is predominantly persistent from smaller communities where there are frequent extinctions of measles between major epidemics. The fundamental mechanisms contributing to this pattern of persistence, which are long-lasting immunity to re-infection, recruitment of susceptibles, seasonality in transmission, age dependence of transmission and the spatial coupling between communities, have all been quantified and, to a greater or lesser level of success, captured by theoretical models. Despite these successes there has not been a consensus over whether simple models can successfully predict the value of the CCS, or indeed which mechanisms determine the persistence of measles over a broader range of population sizes. Specifically, the level of the CCS has been thought to be particularly sensitive to the detailed stochastic dynamics generated by the waiting time distribution (WTD) in the infectious and latent periods. We show that the relative patterns of persistence between models with different WTDs are highly sensitive to the criterion of comparison—in particular, the statistical measure of persistence that is employed. To this end, we introduce two new statistical measures of persitence—fade-outs post epidemic and fade-outs post invasion. Contrary to previous reports, we demonstrate that, no matter the choice of persistence measure, appropriately parametrized models of measles demonstrate similar predictions for the level of the CCS.

Patterns of morbidity and mortality around the globe are determined by interactions between infectious diseases and systematic human socioeconomic processes. The most obvious of these patterns is that the greatest burdens of infectious diseases are found among the poor, who lack the basic resources for disease prevention and treatment. Yet, it is becoming increasingly clear that many infectious diseases are themselves causes of poverty owing to their effects on labour productivity. A particularly subtle phenomenon that receives little attention in the epidemiology literature and is especially important for poor communities is the role of the birth rate as an important direct cause of high disease burdens. Because of their high rates of transmission and life-long immunity, the persistence of many child diseases such as measles relies on high rates of reproduction as their source of susceptible individuals. Thus, there are significant direct health benefits of lower fertility rates, which are further enhanced by interactions with economic processes. Indeed, fertility, poverty and disease all interact with each other in important and predictable ways that can be built into traditional disease ecology models. We present such a model here that provides insights into the long-term effect of policy interventions. For example, because of indirect income effects, herd immunity may be acquired with lower vaccine coverage than previously thought. Reductions in the disease burden can also occur through lower fertility. Our model thus provides a disease ecology framework that is useful for the analysis of demographic transitions.

Understanding the mechanisms that generate oscillations in the incidence of childhood infectious diseases has preoccupied epidemiologists and population ecologists for nearly two centuries. This body of work has generated simple yet powerful explanations for the epidemics of measles and chickenpox, while the dynamics of other infectious diseases, such as whooping cough, have proved more challenging to decipher. A number of authors have, in recent years, proposed that the noisy and somewhat irregular epidemics of whooping cough may arise due to stochasticity and its interaction with nonlinearity in transmission and seasonal variation in contact rates. The reason underlying the susceptibility of whooping cough dynamics to noise and the precise nature of its transient dynamics remain poorly understood. Here we use household data on the incubation period in order to parametrize more realistic distributions of the latent and infectious periods. We demonstrate that previously reported phenomena result from transients following the interaction between the stable annual attractor and unstable multiennial solutions.