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Daniela De Angelis (University of Cambridge) Current Challenges in Inference for Infectious Disease Models Using Data from Multiple Sources

Health-related policy decision-making for epidemic control is increasingly evidence-based, exploiting multiple sources of data. Policy makers rely on models, which are required to approximate realistically the process of interest and use all relevant information. This requirement poses a number of statistically challenging problems. One of these challenges is the computationally efficient estimation of model parameters when the interest is in producing timely assessment and prediction of an epidemic evolution as new data become available.

In this talk current attempts at addressing this computationally efficient parameter estimation problem are discussed in the context of the H1N1 influenza pandemic in England.

Gavin Gibson (Heriot-Watt University) The role of latent processes and functional models in the analysis of partially observed epidemics

This talk will describe new developments in Bayesian model assessment, parameter estimation, and the design of control strategies for epidemic models for partially observed outbreaks. The unifying theme will be the way in which unobserved, or latent processes play a central role in the development of the methods. In the case of model assessment, we will show how functional-model representations of epidemic models can be selected so as to facilitate the construction of latent residual processes, with fixed sampling distributions, which can be used in order to test structural assumptions of the fitted model. We will also demonstrate how such representations can be exploited when attempting to design optimal control strategies for emerging epidemics. Finally we will describe recent developments towards the joint estimation of phylogenetic and epidemic processes in cases where genetic data on pathogens are available in addition to data on disease incidence. The methods will be illustrated using both simulated and real-world data sets. The work is joint with Max Lau, Hola Adrakey, and George Streftaris (HWU), and with Glenn Marion (BioSS).

Theodore Kypraios (University of Nottingham) Bayesian non-parametric inference for epidemic models

Despite the enormous attention given to the development of methods for efficient parameter estimation, there has been relatively little activity in the area of non- parametric inference. That is, drawing inference for the quantities which govern transmission, i) the force of infection and ii) the period during which an individual remains infectious, without making certain modelling assumptions about its (parametric) functional form or that it belongs to a certain family of parametric distributions. In this talk we describe three approaches which allow Bayesian non-parametric inference for the force of infection; namely via Gaussian Processes, Step Functions, and B-splines. We illustrate the proposed methodology with both simulated and real datasets.

Angela Noufaily (The Open University) Detection of Infectious Disease Outbreaks From Laboratory Data With Reporting Delays

Many statistical surveillance systems for the timely detection of outbreaks of infectious disease operate on laboratory data. Such data typically incur reporting delays between the time at which a specimen is collected for diagnostic purposes, and the time at which the results of the laboratory analysis become available. Statistical surveillance systems currently in use usually make some ad-hoc adjustment for such delays, or use counts by time of report. A new statistical approach is proposed taking account of the delays explicitly, by monitoring the number of specimens identified in the current and past m time units, where m is a tuning parameter. The method is studied in the context of an outbreak detection system used in the United Kingdom and several other European countries. A suitable test statistic and its null variance are derived, incorporating uncertainty about the estimated delay distribution. Simulations and applications to some test data sets suggest the method works well, and can improve performance over ad-hoc methods in current use.

Trevelyan J. McKinley (University of Cambridge) A longitudinal model of bovine tuberculosis transmission in Great Britain

Britain spends over £100 million per year in surveillance and compensation for bTB, resulting in costly movement and trade restrictions for farmers. Despite intensive surveillance, considerable uncertainty remains surrounding the true distribution of infection in cattle and wildlife populations. Herds are monitored through slaughterhouse surveillance and regular skin testing, and the frequency of testing for individual herds is based on localised incidence, which acts as a proxy for the risk of infection, but does not account for explicit herd-level characteristics or cattle movements. Surveillance tests are also imperfect, with the lack of a gold-standard diagnostic test making it difficult to estimate levels of unobserved infection. Finally, the lack of detailed information about environmental and wildlife reservoirs makes it challenging to untangle the relative contributions of cattle-to-cattle and spatially localised transmission from other sources.

We address these issues by fitting a Bayesian hierarchical statistical model at the individual animal-level to testing and incidence data. This approach models the hidden transmission process through the use of latent variables, and is fitted using reversible-jump Markov chain Monte Carlo. We estimate the levels of heterogeneity in the risk of infection from cattle-to-cattle transmission compared to introduction from other sources. Our approach potentially allows us to estimate the true efficacies of surveillance tests, as well as the degree of underlying infection, alongside spatially-explicit estimates for the background risk-of-infection from environmental reservoirs.

Tim Kinyanjui (University of Warwick) Information Content of Household-Stratified Epidemics

Household epidemic models have been identified as important tools in the design of targeted vaccination programmes as well as infection prediction. For these models to be of maximum benefit, they require parameterisation from time-series infection data from households. Such data has increasingly become available and in this paper we concern ourselves with the design of studies aimed at collection of such household epidemiological data in order to maximize the amount of information required to calibrate household models. A design decision involves a trade-off between the number of households to enroll and the frequency of sample collection. Two commonly used epidemiological study designs have been considered: cross-sectional design where different households are sampled at every time point and a cohort design where the same households are followed over the course of the study period. The search for optimal design uses Bayesian computational methods to explore the joint parameter-design space combined with the Shannon entropy of the posteriors to estimate the amount of information in each design. For the cross-sectional design, the amount of information increases with the sampling intensity i.e. the designs with the highest number of time-points have the most information. On the other hand, the cohort design achives a trade-off between the number of households sampled and the intensity of follow-up. The robustness of this approach is demonstrated by multiple runs of the designs using different simulated datasets. In general, the results presented do support the current epidemiological designs and we acknowledge that such designs will need to include other factors besides the maximization of information.

Ganna Rozhnova (Utrecht Center for Infection Dynamics) The role of stochasticity in characterizing the dynamics of rubella

Rubella is a completely immunizing and mild infection in children. Understanding its behavior is of considerable applied importance because of Congenital Rubella Syndrome, which results from infection with rubella during early pregnancy and may entail a variety of birth defects. The dynamics of rubella are relatively poorly resolved, and appear to show considerable diversity globally. Here, we investigate the behavior of a stochastic seasonally forced susceptibleinfected-recovered model to characterize the determinants of these dynamics and illustrate patterns by comparison with measles. We perform a systematic analysis of spectra of stochastic fluctuations around stable attractors of the corresponding deterministic model and compare them with spectra from full stochastic simulations in large populations. This approach allows us to quantify the effects of demographic stochasticity and to give a coherent picture of measles and rubella dynamics, explaining essential differences in the patterns exhibited by these diseases. We discuss the implications of our findings in the context of vaccination and changing birth rates as well as the persistence of these two childhood infections.