An epidemic model for an evolving pathogen with strain-dependent immunity.

Between pandemics, the influenza virus exhibits periods of incremental evolution via a process known as antigenic drift. This process gives rise to a sequence of strains of the pathogen that are continuously replaced by newer strains, preventing a build up of immunity in the host population. In this paper, a parsimonious epidemic model is defined that attempts to capture the dynamics of evolving strains within a host population. The 'evolving strains' epidemic model has many properties that lie in-between the Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models, due to the fact that individuals can only be infected by each strain once, but remain susceptible to reinfection by newly emerged strains. Coupling results are used to identify key properties, such as the time to extinction. A range of reproduction numbers are explored to characterise the model, including a novel quasi-stationary reproduction number that can be used to describe the re-emergence of the pathogen into a population with 'average' levels of strain immunity, analogous to the beginning of the winter peak in influenza. Finally the quasi-stationary distribution of the evolving strains model is explored via simulation.

Efficient Real-Time Monitoring of an Emerging Influenza Pandemic: How Feasible?

A prompt public health response to a new epidemic relies on the ability to monitor and predict its evolution in real time as data accumulate. The 2009 A/H1N1 outbreak in the UK revealed pandemic data as noisy, contaminated, potentially biased and originating from multiple sources. This seriously challenges the capacity for real-time monitoring. Here, we assess the feasibility of real-time inference based on such data by constructing an analytic tool combining an age-stratified SEIR transmission model with various observation models describing the data generation mechanisms. As batches of data become available, a sequential Monte Carlo (SMC) algorithm is developed to synthesise multiple imperfect data streams, iterate epidemic inferences and assess model adequacy amidst a rapidly evolving epidemic environment, substantially reducing computation time in comparison to standard MCMC, to ensure timely delivery of real-time epidemic assessments. In application to simulated data designed to mimic the 2009 A/H1N1 epidemic, SMC is shown to have additional benefits in terms of assessing predictive performance and coping with parameter nonidentifiability.

Assessing delivery practices of mothers over time and over space in Uganda, 2003-2012.

BACKGROUND: It is well known that safe delivery in a health facility reduces the risks of maternal and infant mortality resulting from perinatal complications. What is less understood are the factors associated with safe delivery practices. We investigate factors influencing health facility delivery practices while adjusting for multiple other factors simultaneously, spatial heterogeneity, and trends over time. METHODS: We fitted a logistic regression model to Lot Quality Assurance Sampling (LQAS) data from Uganda in a framework that considered individual-level covariates, geographical features, and variations over five time points. We accounted for all two-covariate interactions and all three-covariate interactions for which two of the covariates already had a significant interaction, were able to quantify uncertainty in outputs using computationally intensive cluster bootstrap methods, and displayed outputs using a geographical information system. Finally, we investigated what information could be predicted about districts at future time-points, before the next LQAS survey is carried out. To do this, we applied the model to project a confidence interval for the district level coverage of health facility delivery at future time points, by using the lower and upper end values of known demographics to construct a confidence range for the prediction and define priority groups. RESULTS: We show that ease of access, maternal age and education are strongly associated with delivery in a health facility; after accounting for this, there remains a significant trend towards greater uptake over time. We use this model together with known demographics to formulate a nascent early warning system that identifies candidate districts expected to have low prevalence of facility-based delivery in the immediate future. CONCLUSIONS: Our results support the hypothesis that increased development, particularly related to education and access to health facilities, will act to increase facility-based deliveries, a factor associated with reducing perinatal associated mortality. We provide a statistical method for using inexpensive and routinely collected monitoring and evaluation data to answer complex epidemiology and public health questions in a resource-poor setting. We produced a model based on this data that explained the spatial distribution of facility-based delivery in Uganda. Finally, we used this model to make a prediction about the future priority of districts that was validated by monitoring and evaluation data collected in the next year.

A dynamic model of bovine tuberculosis spread and control in Great Britain.

Bovine tuberculosis (TB) is one of the most complex, persistent and controversial problems facing the British cattle industry, costing the country an estimated £100 million per year. The low sensitivity of the standard diagnostic test leads to considerable ambiguity in determining the main transmission routes of infection, which exacerbates the continuing scientific debate. In turn this uncertainty fuels the fierce public and political disputes on the necessity of controlling badgers to limit the spread of infection. Here we present a dynamic stochastic spatial model for bovine TB in Great Britain that combines within-farm and between-farm transmission. At the farm scale the model incorporates stochastic transmission of infection, maintenance of infection in the environment and a testing protocol that mimics historical government policy. Between-farm transmission has a short-range environmental component and is explicitly driven by movements of individual cattle between farms, as recorded in the Cattle Tracing System. The resultant model replicates the observed annual increase of infection over time as well as the spread of infection into new areas. Given that our model is mechanistic, it can ascribe transmission pathways to each new case; the majority of newly detected cases involve several transmission routes with moving infected cattle, reinfection from an environmental reservoir and poor sensitivity of the diagnostic test all having substantive roles. This underpins our findings on the implications of control measures. Very few of the control options tested have the potential to reverse the observed annual increase, with only intensive strategies such as whole-herd culling or additional national testing proving highly effective, whereas controls focused on a single transmission route are unlikely to be highly effective.

Enhancing Bayesian risk prediction for epidemics using contact tracing.

Contact-tracing data (CTD) collected from disease outbreaks has received relatively little attention in the epidemic modeling literature because it is thought to be unreliable: infection sources might be wrongly attributed, or data might be missing due to resource constraints in the questionnaire exercise. Nevertheless, these data might provide a rich source of information on the disease transmission rate. This paper presents a novel methodology for combining CTD with rate-based contact network data to improve posterior precision, and therefore predictive accuracy. We present an advancement in Bayesian inference for epidemics that assimilates these data and is robust to partial contact tracing. Using a simulation study based on the British poultry industry, we show how the presence of CTD improves posterior predictive accuracy and can directly inform a more effective control strategy.

Networks and the epidemiology of infectious disease.

The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues.

Statistical inference and model selection for the 1861 Hagelloch measles epidemic.

A stochastic epidemic model is proposed which incorporates heterogeneity in the spread of a disease through a population. In particular, three factors are considered: the spatial location of an individual's home and the household and school class to which the individual belongs. The model is applied to an extremely informative measles data set and the model is compared with nested models, which incorporate some, but not all, of the aforementioned factors. A reversible jump Markov chain Monte Carlo algorithm is then introduced which assists in selecting the most appropriate model to fit the data.