Resolving the impact of waiting time distributions on the persistence of measles

Abstract

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.

Conserved patterns of incomplete reporting in pre-vaccine era childhood diseases

“…We find that reporting probabilities vary greatly between disease, geographical region and metapopulation. This variability directly affects patterns of observed extinctions or 'fade-outs' [2,11,38] and, if not addressed, makes comparisons between diseases and metapopulations difficult.…”

“…Several works have explicitly incorporated estimation of incomplete and variable reporting into dynamical models of populations [6,17] and metapopulations [7]. Nonetheless, disease reporting (and variability thereof ) has been largely absent from modern population and metapopulation models that studied stochastic extinction and disease persistence in E&W [11,[24][25][26]. These models (and results) do not necessarily generalize to metapopulations with lower and more variable reporting, such as the pre-vaccine US or modern sub-Saharan Africa.…”

“…Yet, the proposed measures (e.g. [11]) depend on a priori threshold values. Further, the performance of these measures under low and variable disease reporting is not well characterized.…”

“…To address these concerns, Bartlett [2] employed a three-week period of observed extinction, termed fade-out. Conlan et al [11] propose several alternate measures on mechanistic grounds, including fade-outs post invasion and fade-outs post epidemic. Yet, the proposed measures (e.g.…”

A century of transitions in New York City's measles dynamics

“…There has been considerable debate in recent years concerning the most appropriate formulation of the SIR model for childhood infections such as measles [20][21][22][23][24][25][26]. We follow Krylova & Earn [6,27], who showed that for measles, the simplest sinusoidally forced SIR model-when suitably parametrized-makes identical predictions to more complicated versions of the model that include realistically distributed latent and infectious periods (details in §3.1).…”