Plug-and-play inference for disease dynamics: measles in large and small populations as a case study

Abstract

Statistical inference for mechanistic models of partially observed dynamic systems is an active area of research. Most existing inference methods place substantial restrictions upon the form of models that can be fitted and hence upon the nature of the scientific hypotheses that can be entertained and the data that can be used to evaluate them. In contrast, the so-called plug-and-play methods require only simulations from a model and are thus free of such restrictions. We show the utility of the plug-and-play approach in the context of an investigation of measles transmission dynamics. Our novel methodology enables us to ask and answer questions that previous analyses have been unable to address. Specifically, we demonstrate that plug-and-play methods permit the development of a modelling and inference framework applicable to data from both large and small populations. We thereby obtain novel insights into the nature of heterogeneity in mixing and comment on the importance of including extra-demographic stochasticity as a means of dealing with environmental stochasticity and model misspecification. Our approach is readily applicable to many other epidemiological and ecological systems.

Inferring the causes of the three waves of the 1918 influenza pandemic in England and Wales

“…We specify the transmission process with a simple continuous-time compartmental stochastic epidemic model; we use particle filtering and likelihood-based inference [29] to test our model and estimate the parameters.…”

“…We use sequential Monte Carlo methods [28,29] to construct statistical fits of our dynamic models to a 1918 mortality dataset that covers 334 administrative units in the UK (333 distinct areas in England and Wales, including the boroughs of London, and London as a whole).…”

A dynamic dose–response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax

“…Inference was done by fitting a spline curve through the values of the negative log likelihood for each a value creating a smooth depiction of the log likelihood space. Using the minimum value of the spline (the overall maximum likelihood estimate (MLE) fit), we defined a critical cut-off using the likelihood ratio test [14]. That is, at the 95 per cent significance level, the confidence interval of a falls in the range of the minimum log likelihood…”

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

“…Yet, stochastic extinction is not easily distinguished from incomplete reporting. 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].…”

“…For human diseases such as measles, cities comprise the basic epidemiological units of observation over which disease reporting probabilities are typically assumed to be consistent. Reporting of human infectious diseases is known to be both imperfect and variable between cities [13][14][15][16][17][18]. A reporting probability (the proportion of true infections recorded as official case reports, commonly referred to as 'reporting rate') can be estimated for acute, highly infectious diseases that confer permanent immunity, using a combination of demographic and case report data.…”