Bayesian analysis of experimental epidemics of foot-and-mouth disease

What can phylodynamics bring to animal health research?

Infectious diseases are a major burden to global economies, and public and animal health. To date, quantifying the spread of infectious diseases to inform policy making has traditionally relied on epidemiological data collected during epidemics. However, interest has grown in recent phylodynamic techniques to infer pathogen transmission dynamics from genetic data. Here, we provide examples of where this new discipline has enhanced disease management in public health and illustrate how it could be further applied in animal health. In particular, we describe how phylodynamics can address fundamental epidemiological questions, such as inferring key transmission parameters in animal populations and quantifying spillover events at the wildlife-livestock interface, and generate important insights for the design of more effective control strategies.

Latent likelihood ratio tests for assessing spatial kernels in epidemic models

One of the most important issues in the critical assessment of spatio-temporal stochastic models for epidemics is the selection of the transmission kernel used to represent the relationship between infectious challenge and spatial separation of infected and susceptible hosts. As the design of control strategies is often based on an assessment of the distance over which transmission can realistically occur and estimation of this distance is very sensitive to the choice of kernel function, it is important that models used to inform control strategies can be scrutinised in the light of observation in order to elicit possible evidence against the selected kernel function. While a range of approaches to model criticism is in existence, the field remains one in which the need for further research is recognised. In this paper, building on earlier contributions by the authors, we introduce a new approach to assessing the validity of spatial kernels—the latent likelihood ratio tests—which use likelihood-based discrepancy variables that can be used to compare the fit of competing models, and compare the capacity of this approach to detect model mis-specification with that of tests based on the use of infection-link residuals. We demonstrate that the new approach can be used to formulate tests with greater power than infection-link residuals to detect kernel mis-specification particularly when the degree of mis-specification is modest. This new tests avoid the use of a fully Bayesian approach which may introduce undesirable complications related to computational complexity and prior sensitivity.

Integrating data mining and transmission theory in the ecology of infectious diseases

Our understanding of ecological processes is built on patterns inferred from data. Applying modern analytical tools such as machine learning to increasingly high dimensional data offers the potential to expand our perspectives on these processes, shedding new light on complex ecological phenomena such as pathogen transmission in wild populations. Here, we propose a novel approach that combines data mining with theoretical models of disease dynamics. Using rodents as an example, we incorporate statistical differences in the life history features of zoonotic reservoir hosts into pathogen transmission models, enabling us to bound the range of dynamical phenomena associated with hosts, based on their traits. We then test for associations between equilibrium prevalence, a key epidemiological metric and data on human outbreaks of rodent-borne zoonoses, identifying matches between empirical evidence and theoretical predictions of transmission dynamics. We show how this framework can be generalized to other systems through a rubric of disease models and parameters that can be derived from empirical data. By linking life history components directly to their effects on disease dynamics, our mining-modelling approach integrates machine learning and theoretical models to explore mechanisms in the macroecology of pathogen transmission and their consequences for spillover infection to humans.

Bayesian inference of epidemiological parameters from transmission experiments

Epidemiological parameters for livestock diseases are often inferred from transmission experiments. However, there are several limitations inherent to the design of such experiments that limits the precision of parameter estimates. In particular, infection times and latent periods cannot be directly observed and infectious periods may also be censored. We present a Bayesian framework accounting for these features directly and employ Markov chain Monte Carlo techniques to provide robust inferences and quantify the uncertainty in our estimates. We describe the transmission dynamics using a susceptible-exposed-infectious-removed compartmental model, with gamma-distributed transition times. We then fit the model to published data from transmission experiments for foot-and-mouth disease virus (FMDV) and African swine fever virus (ASFV). Where the previous analyses of these data made various assumptions on the unobserved processes in order to draw inferences, our Bayesian approach includes the unobserved infection times and latent periods and quantifies them along with all other model parameters. Drawing inferences about infection times helps identify who infected whom and can also provide insights into transmission mechanisms. Furthermore, we are able to use our models to measure the difference between the latent periods of inoculated and contact-challenged animals and to quantify the effect vaccination has on transmission.

A tutorial introduction to Bayesian inference for stochastic epidemic models using Approximate Bayesian Computation

Likelihood-based inference for disease outbreak data can be very challenging due to the inherent dependence of the data and the fact that they are usually incomplete. In this paper we review recent Approximate Bayesian Computation (ABC) methods for the analysis of such data by fitting to them stochastic epidemic models without having to calculate the likelihood of the observed data. We consider both non-temporal and temporal-data and illustrate the methods with a number of examples featuring different models and datasets. In addition, we present extensions to existing algorithms which are easy to implement and provide an improvement to the existing methodology. Finally, R code to implement the algorithms presented in the paper is available on https://github.com/kypraios/epiABC.

Early-life hepatitis e infection in pigs: the importance of maternally-derived antibodies

Passive immunity (PI), acquired through colostrum intake, is essential for piglet protection against pathogens. Maternally-derived antibodies (MDAs) can decrease the transmission of pathogens between individuals by reducing shedding from infected animals and/or susceptibility of naïve animals. Only a limited number of studies, however, have been carried out to quantify the level of protection conferred by PI in terms of transmission. In the present study, an original modeling framework was designed to estimate parameters governing the transmission of infectious agents in the presence and absence of PI. This epidemiological model accounts for the distribution of PI duration and two different forces of infection depending on the serological status of animals after colostrum intake. A Bayesian approach (Metropolis-Hastings algorithm) was used for parameter estimation. The impact of PI on hepatitis E virus transmission in piglets was investigated using longitudinal serological data from six pig farms. A strong impact of PI was highlighted, the efficiency of transmission being on average 13 times lower in piglets with maternally-derived antibodies than in fully susceptible animals (range: 5–21). Median infection-free survival ages, based on herd-specific estimates, ranged between 8.7 and 13.8 weeks in all but one herd. Indeed, this herd exhibited a different profile with a relatively low prevalence of infected pigs (50% at slaughter age) despite the similar proportions of passively immune individuals after colostrum intake. These results suggest that the age at HEV infection is not strictly dependent upon the proportion of piglets with PI but is also linked to farm-specific husbandry (mingling of piglets after weaning) and hygiene practices. The original methodology developed here, using population-based longitudinal serological data, was able to demonstrate the relative impact of MDAs on the transmission of infectious agents.

Bayesian inference for an emerging arboreal epidemic in the presence of control

The spread of Huanglongbing through citrus groves is used as a case study for modeling an emerging epidemic in the presence of a control. Specifically, the spread of the disease is modeled as a susceptible-exposed-infectious-detected-removed epidemic, where the exposure and infectious times are not observed, detection times are censored, removal times are known, and the disease is spreading through a heterogeneous host population with trees of different age and susceptibility. We show that it is possible to characterize the disease transmission process under these conditions. Two innovations in our work are (i) accounting for control measures via time dependence of the infectious process and (ii) including seasonal and host age effects in the model of the latent period. By estimating parameters in different subregions of a large commercially cultivated orchard, we establish a temporal pattern of invasion, host age dependence of the dispersal parameters, and a close to linear relationship between primary and secondary infectious rates. The model can be used to simulate Huanglongbing epidemics to assess economic costs and potential benefits of putative control scenarios.

Analysis of differential gene expression and novel transcript units of ovine muscle transcriptomes

In this study, we characterized differentially expressed genes (DEGs) between the muscle transcriptomes of Small-tailed Han sheep and Dorper sheep and predicted novel transcript units using high-throughput RNA sequencing technology. Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) analyses showed that 1,300 DEGs were involved in cellular processes, metabolic pathways, and the actin cytoskeleton pathway. Importantly, we identified 34 DEGs related to muscle cell development and differentiation. Additionally, we were able to optimize the gene structure and predict the untranslated regions (UTRs) for some of the DEGs. Among the 123,678 novel predicted transcript units (TUs), 15,015 units were predicted protein sequences. The reliability of the sequencing data was verified through qRT-PCR analysis of 12 genes. These results will provide useful information for functional genetic research in the future.

New model diagnostics for spatio-temporal systems in epidemiology and ecology

A cardinal challenge in epidemiological and ecological modelling is to develop effective and easily deployed tools for model assessment. The availability of such methods would greatly improve understanding, prediction and management of disease and ecosystems. Conventional Bayesian model assessment tools such as Bayes factors and the deviance information criterion (DIC) are natural candidates but suffer from important limitations because of their sensitivity and complexity. Posterior predictive checks, which use summary statistics of the observed process simulated from competing models, can provide a measure of model fit but appropriate statistics can be difficult to identify. Here, we develop a novel approach for diagnosing mis-specifications of a general spatio-temporal transmission model by embedding classical ideas within a Bayesian analysis. Specifically, by proposing suitably designed non-centred parametrization schemes, we construct latent residuals whose sampling properties are known given the model specification and which can be used to measure overall fit and to elicit evidence of the nature of mis-specifications of spatial and temporal processes included in the model. This model assessment approach can readily be implemented as an addendum to standard estimation algorithms for sampling from the posterior distributions, for example Markov chain Monte Carlo. The proposed methodology is first tested using simulated data and subsequently applied to data describing the spread of Heracleum mantegazzianum (giant hogweed) across Great Britain over a 30-year period. The proposed methods are compared with alternative techniques including posterior predictive checking and the DIC. Results show that the proposed diagnostic tools are effective in assessing competing stochastic spatio-temporal transmission models and may offer improvements in power to detect model mis-specifications. Moreover, the latent-residual framework introduced here extends readily to a broad range of ecological and epidemiological models.

Modelling under-reporting in epidemics

Under-reporting of infected cases is crucial for many diseases because of the bias it can introduce when making inference for the model parameters. The objective of this paper is to study the effect of under-reporting in epidemics by considering the stochastic Markovian SIR epidemic in which various reporting processes are incorporated. In particular, we first investigate the effect on the estimation process of ignoring under-reporting when it is present in an epidemic outbreak. We show that such an approach leads to under-estimation of the infection rate and the reproduction number. Secondly, by allowing for the fact that under-reporting is occurring, we develop suitable models for estimation of the epidemic parameters and explore how well the reporting rate and other model parameters can be estimated. We consider the case of a constant reporting probability and also more realistic assumptions which involve the reporting probability depending on time or the source of infection for each infected individual. Due to the incomplete nature of the data and reporting process, the Bayesian approach provides a natural modelling framework and we perform inference using data augmentation and reversible jump Markov chain Monte Carlo techniques.

Spatial approximations of network-based individual level infectious disease models

Often, when modeling infectious disease spread, the complex network through which the disease propagates is approximated by simplified spatial information. Here, we simulate epidemic spread through various contact networks and fit spatial-based models in a Bayesian framework using Markov chain Monte Carlo methods. These spatial models are individual-level models which account for the spatio-temporal dynamics of infectious disease. The focus here is on choosing a spatial model which best predicts the true probabilities of infection, as well as determining under which conditions such spatial models fail. Spatial models tend to predict infection probability reasonably well when disease spread is propagated through contact networks in which contacts are only within a certain distance of each other. If contacts exist over long distances, the spatial models tend to perform worse when compared to the network model.

A path-specific SEIR model for use with general latent and infectious time distributions

Most current Bayesian SEIR (Susceptible, Exposed, Infectious, Removed (or Recovered)) models either use exponentially distributed latent and infectious periods, allow for a single distribution on the latent and infectious period, or make strong assumptions regarding the quantity of information available regarding time distributions, particularly the time spent in the exposed compartment. Many infectious diseases require a more realistic assumption on the latent and infectious periods. In this article, we provide an alternative model allowing general distributions to be utilized for both the exposed and infectious compartments, while avoiding the need for full latent time data. The alternative formulation is a path-specific SEIR (PS SEIR) model that follows individual paths through the exposed and infectious compartments, thereby removing the need for an exponential assumption on the latent and infectious time distributions. We show how the PS SEIR model is a stochastic analog to a general class of deterministic SEIR models. We then demonstrate the improvement of this PS SEIR model over more common population averaged models via simulation results and perform a new analysis of the Iowa mumps epidemic from 2006.

Applications of percolation theory to fungal spread with synergy

There is increasing interest in the use of the percolation paradigm to analyse and predict the progress of disease spreading in spatially structured populations of animals and plants. The wider utility of the approach has been limited, however, by several restrictive assumptions, foremost of which is a strict requirement for simple nearest-neighbour transmission, in which the disease history of an individual is influenced only by that of its neighbours. In a recent paper, the percolation paradigm has been generalized to incorporate synergistic interactions in host infectivity and susceptibility, and the impact of these interactions on the invasive dynamics of an epidemic has been demonstrated. In the current paper, we elicit evidence that such synergistic interactions may underlie transmission dynamics in real-world systems by first formulating a model for the spread of a ubiquitous parasitic and saprotrophic fungus through replicated populations of nutrient sites and subsequently fitting and testing the model using data from experimental microcosms. Using Bayesian computational methods for model fitting, we demonstrate that synergistic interactions are necessary to explain the dynamics observed in the replicate experiments. The broader implications of this work in identifying disease-control strategies that deflect epidemics from invasive to non-invasive regimes are discussed.

Non-exponential tolerance to infection in epidemic systems--modeling, inference, and assessment

The transmission dynamics of infectious diseases have been traditionally described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance following the Sellke construction. Here we focus on a generalization using Weibull individual tolerance thresholds under the susceptible-exposed-infectious-removed class of models which is widely employed in epidemics. Applications with experimental foot-and-mouth disease and historical smallpox data are discussed, and simulation results are presented. Inference is carried out using Markov chain Monte Carlo methods following a Bayesian approach. Model evaluation is performed, where the adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, and comparison between 2 candidate models is also considered using a latent likelihood ratio-type test that avoids problems encountered with relevant methods based on Bayes factors.

Modelling and inference for epidemic models featuring non-linear infection pressure

We consider a Susceptible-Infective-Removed (SIR) stochastic epidemic model in which the infection rate is of the form βN⁻¹X(t)Y(t)(α). It is demonstrated that both the threshold behaviour of this model and the behaviour of the corresponding deterministic model differ markedly from the standard SIR model (i.e. α=1). Methods of statistical inference for this model are described, given outbreak data, and the extent to which all three model parameters can be estimated is considered.

Outbreaks of H5N1 in poultry in Thailand: the relative role of poultry production types in sustaining transmission and the impact of active surveillance in control

H5N1, highly pathogenic avian influenza, continues to pose a public health risk in the countries of southeast Asia where it has become endemic. However, in Thailand, which experienced two of the largest recorded epidemics in 2004-2005, the disease has been successfully reduced to very low levels. We fitted a spatio-temporal model of the spread of infection to outbreak data collected during the second wave of outbreaks to assess the extent to which different poultry types were responsible for propagating infection. Our estimates suggest that the wave of outbreaks would not have been possible without the contribution of backyard flocks to the susceptibility of a sub-district. However, we also estimated that outbreaks involving commercial poultry, a much larger sector in Thailand than in neighbouring countries, were disproportionately infectious, a factor which was also crucial in sustaining the wave. As a result, implemented measures that aim to reduce the role of commercial farms in the spread of infection, such as the drive to bring aspects of the supply chain 'in house', may help to explain the subsequent success in controlling H5N1 in Thailand. We also found that periods of active surveillance substantially improved the rate of outbreak detection.

A single vaccination of commercial broilers does not reduce transmission of H5N1 highly pathogenic avian influenza

Vaccination of chickens has become routine practice in Asian countries in which H5N1 highly pathogenic avian influenza (HPAI) is endemically present. This mainly applies to layer and breeder flocks, but broilers are usually left unvaccinated. Here we investigate whether vaccination is able to reduce HPAI H5N1 virus transmission among broiler chickens. Four sets of experiments were carried out, each consisting of 22 replicate trials containing a pair of birds. Experiments 1-3 were carried out with four-week-old birds that were unvaccinated, and vaccinated at day 1 or at day 10 of age. Experiment 4 was carried out with unvaccinated day-old broiler chicks. One chicken in each trial was inoculated with H5N1 HPAI virus. One chicken in each trial was inoculated with virus. The course of the infection chain was monitored by serological analysis, and by virus isolation performed on tracheal and cloacal swabs. The analyses were based on a stochastic SEIR model using a Bayesian inferential framework. When inoculation was carried out at the 28^th day of life, transmission was efficient in unvaccinated birds, and in birds vaccinated at first or tenth day of life. In these experiments estimates of the latent period (~1.0 day), infectious period (~3.3 days), and transmission rate parameter (~1.4 per day) were similar, as were estimates of the reproduction number (~4) and generation interval (~1.4 day). Transmission was significantly less efficient in unvaccinated chickens when inoculation was carried out on the first day of life. These results show that vaccination of broiler chickens does not reduce transmission, and suggest that this may be due to the interference of maternal immunity.

Statistical inference to advance network models in epidemiology

Contact networks are playing an increasingly important role in the study of epidemiology. Most of the existing work in this area has focused on considering the effect of underlying network structure on epidemic dynamics by using tools from probability theory and computer simulation. This work has provided much insight on the role that heterogeneity in host contact patterns plays on infectious disease dynamics. Despite the important understanding afforded by the probability and simulation paradigm, this approach does not directly address important questions about the structure of contact networks such as what is the best network model for a particular mode of disease transmission, how parameter values of a given model should be estimated, or how precisely the data allow us to estimate these parameter values. We argue that these questions are best answered within a statistical framework and discuss the role of statistical inference in estimating contact networks from epidemiological data.

From phenotype to genotype: a Bayesian solution

The study of biological systems commonly depends on inferring the state of a 'hidden' variable, such as an underlying genotype, from that of an 'observed' variable, such as an expressed phenotype. However, this cannot be achieved using traditional quantitative methods when more than one genetic mechanism exists for a single observable phenotype. Using a novel latent class Bayesian model, it is possible to infer the prevalence of different genetic elements in a population given a sample of phenotypes. As an exemplar, data comprising phenotypic resistance to six antimicrobials obtained from passive surveillance of Salmonella Typhimurium DT104 are analysed to infer the prevalence of individual resistance genes, as well as the prevalence of a genomic island known as SGI1 and its variants. Three competing models are fitted to the data and distinguished between using posterior predictive p-values to assess their ability to predict the observed number of unique phenotypes. The results suggest that several SGI1 variants circulate in a few fixed forms through the population from which our data were derived. The methods presented could be applied to other types of phenotypic data, and represent a useful and generic mechanism of inferring the genetic population structure of organisms.

Spread of Q fever within dairy cattle herds: key parameters inferred using a Bayesian approach

Q fever is a worldwide zoonosis caused by Coxiella burnetii. Although ruminants are recognized as the most important source of human infection, no previous studies have focused on assessing the characteristics of the bacterial spread within a cattle herd and no epidemic model has been proposed in this context. We assess the key epidemiological parameters from field data in a Bayesian framework that takes into account the available knowledge, missing data and the uncertainty of the observation process owing to the imperfection of diagnostic tests. We propose an original individual-based Markovian model in discrete time describing the evolution of the infection for each animal. Markov chain Monte Carlo methodology is used to estimate parameters of interest from data consisting of individual health states of 217 cows of five chronically infected dairy herds sampled every week for a four-week period. Outputs are the posterior distributions of the probabilities of transition between health states and of the environmental bacterial load. Our findings show that some herds are characterized by a very low infection risk while others have a mild infection risk and a non-negligible intermittent shedding probability. Moreover, the antibody status seems to be a key point in the bacterial spread (shedders with antibodies shed for a longer period of time than shedders without antibodies). In addition to the biological insights, these estimates also provide information for calibrating simulation models to assess control strategies for C. burnetii infection.

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

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.

Cross-disciplinary demands of multihost pathogens

The dynamics of infectious disease spread depend on host population contact structure. Heterogeneities in this contact structure can arise from various forms of demographic and spatial phenomena. Craft et al. (this issue) have constructed an exploratory simulation model of the spread of canine distemper virus through a multispecies carnivore community. Each species in this community is modelled with a contact structure reflecting host social organization, ranging behaviour, and likely interspecific contact patterns. The results are used to infer the possible roles of different species in determining the observed spatio-temporal incidence of canine distemper virus in Serengeti lions during an outbreak in 1993-94.

Estimation of transmission parameters of H5N1 avian influenza virus in chickens

Despite considerable research efforts, little is yet known about key epidemiological parameters of H5N1 highly pathogenic influenza viruses in their avian hosts. Here we show how these parameters can be estimated using a limited number of birds in experimental transmission studies. Our quantitative estimates, based on Bayesian methods of inference, reveal that (i) the period of latency of H5N1 influenza virus in unvaccinated chickens is short (mean: 0.24 days; 95% credible interval: 0.099–0.48 days); (ii) the infectious period of H5N1 virus in unvaccinated chickens is approximately 2 days (mean: 2.1 days; 95%CI: 1.8–2.3 days); (iii) the reproduction number of H5N1 virus in unvaccinated chickens need not be high (mean: 1.6; 95%CI: 0.90–2.5), although the virus is expected to spread rapidly because it has a short generation interval in unvaccinated chickens (mean: 1.3 days; 95%CI: 1.0–1.5 days); and (iv) vaccination with genetically and antigenically distant H5N2 vaccines can effectively halt transmission. Simulations based on the estimated parameters indicate that herd immunity may be obtained if at least 80% of chickens in a flock are vaccinated. We discuss the implications for the control of H5N1 avian influenza virus in areas where it is endemic.

Outbreaks of highly pathogenic H5N1 avian influenza in poultry first occurred in China in 1996. Since that time, the virus has become endemic in Asia, and has been the cause of outbreaks in Africa and Europe. Although many aspects of H5N1 virus biology have been studied in detail, surprisingly little is known about the key epidemiological parameters of the virus in its avian hosts (the length of time from infection until a bird becomes infectious, the duration of infectiousness, how many birds each infectious bird will infect). In this paper we show, using experimental transmission studies with unvaccinated and vaccinated chickens, that H5N1 avian influenza induces a short duration of infectiousness (∼2 days) and a very short period of time from infection until infectiousness (∼0.25 day) in unvaccinated chickens. Furthermore, while transmission was efficient among unvaccinated birds, no bird-to-bird transmission was observed in vaccinated chickens. Our results indicate that it may be difficult to curb outbreaks by vaccination after an introduction in a flock has been detected. On the other hand, preventive vaccination could be effective in preventing virus introductions and limiting the size of outbreaks.

Epidemiological inference for partially observed epidemics: the example of the 2001 foot and mouth epidemic in Great Britain

This paper develops a statistical framework for a retrospective analysis for well-observed livestock epidemics during which intervention policies may conceal cases, thus potentially biasing naively derived parameter and final size estimates. We apply the methods to the 2001 foot and mouth epidemic (FMD) in Great Britain, during which a large number of farms (about 7500) were pre-emptively culled as part of the control effort without ever being diagnosed as being infected. We infer farm-level infectivity and susceptibility parameters, a distribution for the delay from infection to report, together with a time varying farm infectivity profile for farms. Hidden infections among proactively culled farms were accounted for using a data augmentation approach utilising reversible jump MCMC methods. Simulated epidemics derived using the parameter estimates obtained reproduced the 2001 epidemic well. Our analysis demonstrates that time-varying infectivity profiles fit the 2001 data better than naive assumptions of constant infectiousness. We estimate that around 210 (or 2.8%) of the farms proactively culled in the 2001 epidemic were infected. However, for the parameter estimated obtained, preliminary simulation results indicate that had contiguous culling not been applied in 2001, the epidemic might have been substantially larger.

Transmission parameters of the 2001 foot and mouth epidemic in Great Britain

Despite intensive ongoing research, key aspects of the spatial-temporal evolution of the 2001 foot and mouth disease (FMD) epidemic in Great Britain (GB) remain unexplained. Here we develop a Markov Chain Monte Carlo (MCMC) method for estimating epidemiological parameters of the 2001 outbreak for a range of simple transmission models. We make the simplifying assumption that infectious farms were completely observed in 2001, equivalent to assuming that farms that were proactively culled but not diagnosed with FMD were not infectious, even if some were infected. We estimate how transmission parameters varied through time, highlighting the impact of the control measures on the progression of the epidemic. We demonstrate statistically significant evidence for assortative contact patterns between animals of the same species. Predictive risk maps of the transmission potential in different geographic areas of GB are presented for the fitted models.

Quantification of the effect of vaccination on transmission of avian influenza (H7N7) in chickens

Recent outbreaks of highly pathogenic avian influenza (HPAI) viruses in poultry and their threatening zoonotic consequences emphasize the need for effective control measures. Although vaccination of poultry against avian influenza provides a potentially attractive control measure, little is known about the effect of vaccination on epidemiologically relevant parameters, such as transmissibility and the infectious period. We used transmission experiments to study the effect of vaccination on the transmission characteristics of HPAI A/Chicken/Netherlands/03 H7N7 in chickens. In the experiments, a number of infected and uninfected chickens is housed together and the infection chain is monitored by virus isolation and serology. Analysis is based on a stochastic susceptible, latently infected, infectious, recovered (SEIR) epidemic model. We found that vaccination is able to reduce the transmission level to such an extent that a major outbreak is prevented, important variables being the type of vaccine (H7N1 or H7N3) and the moment of challenge after vaccination. Two weeks after vaccination, both vaccines completely block transmission. One week after vaccination, the H7N1 vaccine is better than the H7N3 vaccine at reducing the spread of the H7N7 virus. We discuss the implications of these findings for the use of vaccination programs in poultry and the value of transmission experiments in the process of choosing vaccine.