Simulation-based Bayesian inference for epidemic models

This is the author pre-print version. The final version is available from the publisher via the DOI in this record.A powerful and flexible method for fitting dynamic models to missing and censored data is to use the Bayesian paradigm via data-augmented Markov chain Monte Carlo (DA-MCMC). This samples from the joint posterior for the parameters and missing data, but requires high memory overheads for large-scale systems. In addition, designing efficient proposal distributions for the missing data is typically challenging. Pseudo-marginal methods instead integrate across the missing data using a Monte Carlo estimate for the likelihood, generated from multiple independent simulations from the model. These techniques can avoid the high memory requirements of DA-MCMC, and under certain conditions produce the exact marginal posterior distribution for parameters. A novel method is presented for implementing importance sampling for dynamic epidemic models, by conditioning the simulations on sets of validity criteria (based on the model structure) as well as the observed data. The flexibility of these techniques is illustrated using both removal time and final size data from an outbreak of smallpox. It is shown that these approaches can circumvent the need for reversible-jump MCMC, and can allow inference in situations where DA-MCMC is impossible due to computationally infeasible likelihoods. © 2013 Elsevier B.V. All rights reserved.T. J. M. was in part supported by Department for the Environment, Food and Rural Affairs/Higher Education Funding Council of England, grant number VT0105 and BBSRC grant (BB/I012192/1). J. V. R was in part supported by Australian Research Council’s Discovery Projects funding scheme (project number DP110102893). R. D. was in part supported by Natural Sciences and Engineering Research Council (NSERC) of Canada’s Discovery Grants Program. A. R. C. was in part supported by National Medical Research Council (NMRC/HINIR/005/2009) and NUS Initiative to Improve Health in Asia. The authors would like to thank Andrew Conlan and Theo Kypraios for useful discussions

Topographic determinants of foot and mouth disease transmission in the UK 2001 epidemic

Background A key challenge for modelling infectious disease dynamics is to understand the spatial spread of infection in real landscapes. This ideally requires a parallel record of spatial epidemic spread and a detailed map of susceptible host density along with relevant transport links and geographical features. Results Here we analyse the most detailed such data to date arising from the UK 2001 foot and mouth epidemic. We show that Euclidean distance between infectious and susceptible premises is a better predictor of transmission risk than shortest and quickest routes via road, except where major geographical features intervene. Conclusion Thus, a simple spatial transmission kernel based on Euclidean distance suffices in most regions, probably reflecting the multiplicity of transmission routes during the epidemic

How to make predictions about future infectious disease risks

Formal, quantitative approaches are now widely used to make predictions about the likelihood of an infectious disease outbreak, how the disease will spread, and how to control it. Several well-established methodologies are available, including risk factor analysis, risk modelling and dynamic modelling. Even so, predictive modelling is very much the ‘art of the possible’, which tends to drive research effort towards some areas and away from others which may be at least as important. Building on the undoubted success of quantitative modelling of the epidemiology and control of human and animal diseases such as AIDS, influenza, foot-and-mouth disease and BSE, attention needs to be paid to developing a more holistic framework that captures the role of the underlying drivers of disease risks, from demography and behaviour to land use and climate change. At the same time, there is still considerable room for improvement in how quantitative analyses and their outputs are communicated to policy makers and other stakeholders. A starting point would be generally accepted guidelines for ‘good practice’ for the development and the use of predictive models

Disease prevention versus data privacy : using landcover maps to inform spatial epidemic models

The availability of epidemiological data in the early stages of an outbreak of an infectious disease is vital for modelers to make accurate predictions regarding the likely spread of disease and preferred intervention strategies. However, in some countries, the necessary demographic data are only available at an aggregate scale. We investigated the ability of models of livestock infectious diseases to predict epidemic spread and obtain optimal control policies in the event of imperfect, aggregated data. Taking a geographic information approach, we used land cover data to predict UK farm locations and investigated the influence of using these synthetic location data sets upon epidemiological predictions in the event of an outbreak of foot-and-mouth disease. When broadly classified land cover data were used to create synthetic farm locations, model predictions deviated significantly from those simulated on true data. However, when more resolved subclass land use data were used, moderate to highly accurate predictions of epidemic size, duration and optimal vaccination and ring culling strategies were obtained. This suggests that a geographic information approach may be useful where individual farm-level data are not available, to allow predictive analyses to be carried out regarding the likely spread of disease. This method can also be used for contingency planning in collaboration with policy makers to determine preferred control strategies in the event of a future outbreak of infectious disease in livestock

Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, whenand to whom to apply an intervention.We develop a framework for using data to informthese decisionsin realtime.We formalize a treatment allocation strategy as a sequence of functions, oneper treatment period, that map up-to-date information on the spread of an infectious diseaseto a subset of locations where treatment should be allocated. An optimal allocation strategyoptimizes some cumulative outcome, e.g. the number of uninfected locations, the geographicfootprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategyfor an emerging infectious disease is challenging because spatial proximity induces interferencebetween locations, the number of possible allocations is exponential in the number oflocations, and because disease dynamics and intervention effectiveness are unknown at outbreak.We derive a Bayesian on-line estimator of the optimal allocation strategy that combinessimulation–optimization with Thompson sampling.The estimator proposed performs favourablyin simulation experiments. This work is motivated by and illustrated using data on the spread ofwhite nose syndrome, which is a highly fatal infectious disease devastating bat populations inNorth America

Rapid simulation of spatial epidemics: A spectral method

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended ‘image’ of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel

Epidemic reconstruction in a Phylogenetics framework:Transmission trees as partitions of the node set

The reconstruction of transmission trees for epidemics from genetic data has been the subject of some recent interest. It has been demonstrated that the transmission tree structure can be investigated by augmenting internal nodes of a phylogenetic tree constructed using pathogen sequences from the epidemic with information about the host that held the corresponding lineage. In this paper, we note that this augmentation is equivalent to a correspondence between transmission trees and partitions of the phylogenetic tree into connected subtrees each containing one tip, and provide a framework for Markov Chain Monte Carlo inference of phylogenies that are partitioned in this way, giving a new method to co-estimate both trees. The procedure is integrated in the existing phylogenetic inference package BEAST.Comment: 40 pages, 3 figure

Accuracy of models for the 2001 foot-and-mouth epidemic

Since 2001 models of the spread of foot-and-mouth disease, supported by the data from the UK epidemic, have been expounded as some of the best examples of problem-driven epidemic models. These claims are generally based on a comparison between model results and epidemic data at fairly coarse spatio-temporal resolution. Here, we focus on a comparison between model and data at the individual farm level, assessing the potential of the model to predict the infectious status of farms in both the short and long terms. Although the accuracy with which the model predicts farms reporting infection is between 5 and 15%, these low levels are attributable to the expected level of variation between epidemics, and are comparable to the agreement between two independent model simulations. By contrast, while the accuracy of predicting culls is higher (20-30%), this is lower than expected from the comparison between model epidemics. These results generally support the contention that the type of the model used in 2001 was a reliable representation of the epidemic process, but highlight the difficulties of predicting the complex human response, in terms of control strategies to the perceived epidemic risk

An industry wage curve

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