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

Ongoing estimation of the epidemic parameters of a stochastic, spatial, discrete-time model for a 1983-84 avian influenza epidemic

We formulate a stochastic, spatial, discrete-time model of viral "Susceptible, Exposed, Infectious, Recovered" animal epidemics and apply it to an avian influenza epidemic in Pennsylvania in 1983-84. Using weekly data for the number of newly infectious cases collected during the epidemic, we find estimates for the latent period of the virus and the values of two parameters within the transmission kernel of the model. These data are then jackknifed on a progressive weekly basis to show how our estimates can be applied to an ongoing epidemic to generate continually improving values of certain epidemic parameters.

Bayesian analysis of animal movements related to factors at herd and between herd levels: Implications for disease spread modeling

A method to assess the influence of between herd distances, production types and herd sizes on patterns of between herd contacts is presented. It was applied on pig movement data from a central database of the Swedish Board of Agriculture. To determine the influence of these factors on the contact between holdings we used a Bayesian model and Markov chain Monte Carlo (MCMC) methods to estimate the posterior distribution of model parameters. The analysis showed that the contact pattern via animal movements is highly heterogeneous and influenced by all three factors, production type, herd size, and distance between holdings. Most production types showed a positive relationship between maximum capacity and the probability of both incoming and outgoing movements. In agreement with previous studies, holdings also differed in both the number of contacts as well as with what holding types contact occurred with. Also, the scale and shape of distance dependence in contact probability was shown to differ depending on the production types of holdings.To demonstrate how the methodology may be used for risk assessment, disease transmissions via animal movements were simulated with the model used for analysis of contacts, and parameterized by the analyzed posterior distribution. A Generalized Linear Model showed that herds with production types Sow pool center, Multiplying herd and Nucleus herd have higher risk of generating a large number of new infections. Multiplying herds are also expected to generate many long distance transmissions, while transmissions generated by Sow pool centers are confined to more local areas. We argue that the methodology presented may be a useful tool for improvement of risk assessment based on data found in central databases.

Escherichia coli O157 infection on Scottish cattle farms: dynamics and control

In this study, we parametrize a stochastic individual-based model of the transmission dynamics of Escherichia coli O157 infection among Scottish cattle farms and use the model to predict the impacts of both targeted and non-targeted interventions. We first generate distributions of model parameter estimates using Markov chain Monte Carlo methods. Despite considerable uncertainty in parameter values, each set of parameter values within the 95th percentile range implies a fairly similar impact of interventions. Interventions that reduce the transmission coefficient and/or increase the recovery rate of infected farms (e.g. via vaccination and biosecurity) are much more effective in reducing the level of infection than reducing cattle movement rates, which improves effectiveness only when the overall control effort is small. Targeted interventions based on farm-level risk factors are more efficient than non-targeted interventions. Herd size is a major determinant of risk of infection, and our simulations confirmed that targeting interventions at farms with the largest herds is almost as effective as targeting based on overall risk. However, because of the striking characteristic that the infection force depends weakly on the number of infected farms, no interventions that are less than 100 per cent effective can eradicate E. coli O157 infection from Scottish cattle farms, implying that eliminating the disease is impractical.

The shape of the spatial kernel and its implications for biological invasions in patchy environments

Ecological and epidemiological invasions occur in a spatial context. We investigated how these processes correlate to the distance dependence of spread or dispersal between spatial entities such as habitat patches or epidemiological units. Distance dependence is described by a spatial kernel, characterized by its shape (kurtosis) and width (variance). We also developed a novel method to analyse and generate point-pattern landscapes based on spectral representation. This involves two measures: continuity, which is related to autocorrelation and contrast, which refers to variation in patch density. We also analysed some empirical data where our results are expected to have implications, namely distributions of trees (Quercus and Ulmus) and farms in Sweden. Through a simulation study, we found that kernel shape was not important for predicting the invasion speed in randomly distributed patches. However, the shape may be essential when the distribution of patches deviates from randomness, particularly when the contrast is high. We conclude that the speed of invasions depends on the spatial context and the effect of the spatial kernel is intertwined with the spatial structure. This implies substantial demands on the empirical data, because it requires knowledge of shape and width of the spatial kernel, and spatial structure.

Transmission risks and control of foot-and-mouth disease in The Netherlands: spatial patterns

In 2001 the epidemics of foot-and-mouth disease virus (FMDV) in Great Britain, The Netherlands and France have shown how fast FMDV may spread between farms. The massive socio-economic impact of these epidemics and the intervention measures taken demonstrate the need for quantitative assessments of the efficacy of candidate intervention strategies. Here we use a mathematical model to describe the spatial transmission of FMDV in The Netherlands and use the Dutch 2001 outbreak data to estimate model parameters. We assess the effect of ring culling strategies using a novel and fast approach producing risk maps, and discuss its consequences for ring vaccination. These risk maps identify both the geographical areas of low risk, where a given intervention strategy is likely to achieve epidemic control within only two or three farm-to-farm infection generations, and high-risk areas, where control is likely to take (much) longer. Our results indicate that certain densely populated livestock areas in the Netherlands remain high-risk areas even for strategies that extend EU minimum measures with culling or vaccination within a ring radius of several kilometres. Depending on an economic assessment, area-wide vaccination might be judged appropriate once an FMDV outbreak would have been confirmed in or close to such a high-density area. The modeling approach developed here could be readily applied to outbreak data for other diseases and in other countries.

Impact of spatial clustering on disease transmission and optimal control

Spatial heterogeneities and spatial separation of hosts are often seen as key factors when developing accurate predictive models of the spread of pathogens. The question we address in this paper is how coarse the resolution of the spatial data can be for a model to be a useful tool for informing control policies. We examine this problem using the specific case of foot-and-mouth disease spreading between farms using the formulation developed during the 2001 epidemic in the United Kingdom. We show that, if our model is carefully parameterized to match epidemic behavior, then using aggregate county-scale data from the United States is sufficient to closely determine optimal control measures (specifically ring culling). This result also holds when the approach is extended to theoretical distributions of farms where the spatial clustering can be manipulated to extremes. We have therefore shown that, although spatial structure can be critically important in allowing us to predict the emergent population-scale behavior from a knowledge of the individual-level dynamics, for this specific applied question, such structure is mostly subsumed in the parameterization allowing us to make policy predictions in the absence of high-quality spatial information. We believe that this approach will be of considerable benefit across a range of disciplines where data are only available at intermediate spatial scales.

The role of pre-emptive culling in the control of foot-and-mouth disease

The 2001 foot-and-mouth disease epidemic was controlled by culling of infectious premises and pre-emptive culling intended to limit the spread of disease. Of the control strategies adopted, routine culling of farms that were contiguous to infected premises caused the most controversy. Here we perform a retrospective analysis of the culling of contiguous premises as performed in 2001 and a simulation study of the effects of this policy on reducing the number of farms affected by disease. Our simulation results support previous studies and show that a national policy of contiguous premises (CPs) culling leads to fewer farms losing livestock. The optimal national policy for controlling the 2001 epidemic is found to be the targeting of all contiguous premises, whereas for localized outbreaks in high animal density regions, more extensive fixed radius ring culling is optimal. Analysis of the 2001 data suggests that the lowest-risk CPs were generally prioritized for culling, however, even in this case, the policy is predicted to be effective. A sensitivity analysis and the development of a spatially heterogeneous policy show that the optimal culling level depends upon the basic reproductive ratio of the infection and the width of the dispersal kernel. These analyses highlight an important and probably quite general result: optimal control is highly dependent upon the distance over which the pathogen can be transmitted, the transmission rate of infection and local demography where the disease is introduced.

Statistical modeling of holding level susceptibility to infection during the 2001 foot and mouth disease epidemic in Great Britain

BACKGROUND

An understanding of the factors that determine the risk of members of a susceptible population becoming infected is essential for estimating the potential for disease spread, as opposed to just focusing on transmission from an infected population. Furthermore, analysis of the risk factors can reveal important characteristics of an epidemic and further develop understanding of the processes operating.

METHODS

This paper describes the development of a mixed effects logistic regression model of susceptibility of holdings to foot and mouth disease (FMD) during the 2001 epidemic in Great Britain following the imposition of a national ban on the movements of susceptible animals (NMB).

RESULTS

The principal risk factors identified in the model were shorter distances to the nearest infectious seed (a holding infected before the NMB) and the county of the holding (principally Cumbria). Additional risk factors included holdings that are mixed species rather than single species, the surface area of the holding, and the number of cattle within 10km (all p<0.001), but not surrounding sheep densities (p>0.1). The fit of the model was evaluated using the area under the receiver operator characteristic curve (ROC) and the Hosmer and Lemeshow Chi-squared statistic; the fit was good with both tests (area under the ROC=0.962 and Hosmer and Lemeshow Chi-squared statistic=49.98 (p>0.1)).

CONCLUSIONS

Holdings at greatest risk of infection can be identified using simple readily available risk factors; this information could be employed in the control of future FMD epidemics.

Predicting infection risk of airborne foot-and-mouth disease

Foot-and-mouth disease is a highly contagious disease of cloven-hoofed animals, the control and eradication of which is of significant worldwide socio-economic importance. The virus may spread by direct contact between animals or via fomites as well as through airborne transmission, with the latter being the most difficult to control. Here, we consider the risk of infection to flocks or herds from airborne virus emitted from a known infected premises. We show that airborne infection can be predicted quickly and with a good degree of accuracy, provided that the source of virus emission has been determined and reliable geo-referenced herd data are available. A simple model provides a reliable tool for estimating risk from known sources and for prioritizing surveillance and detection efforts. The issue of data information management systems was highlighted as a lesson to be learned from the official inquiry into the UK 2007 foot-and-mouth outbreak: results here suggest that the efficacy of disease control measures could be markedly improved through an accurate livestock database incorporating flock/herd size and location, which would enable tactical as well as strategic modelling.

Is R(0) a good predictor of final epidemic size: foot-and-mouth disease in the UK

One of the main uses of an epidemic model is to predict the scale of an outbreak from the first few cases. In a homogeneous and non-spatial model there is a straightforward relationship between the basic reproductive ratio, R(0), and the final epidemic size; however when there is a significant spatial component to disease spread and the population is heterogeneous predicting how the epidemic size varies with the initial source of infection is far more complex. Here we use a well-developed spatio-temporal model of the spread of foot-and-mouth disease, parameterized to match the 2001 UK outbreak, to address the relationship between the scale of the epidemic and the nature of the initially infected farm. We show that there is considerable heterogeneity in both the likelihood of a epidemic and the epidemic impact (total number of farms losing livestock to either infection or control) and that these two elements are best captured by measurements at different spatial scales. The likelihood of an epidemic can be predicted from a knowledge of the reproduction ratio of the initial farm (R(i)), whereas the epidemic impact conditional on an epidemic occurring is best predicted by averaging the second-generation reproduction ratio (R(i)((2))) in a 58 km ring around the infected farm. Combining these two predictions provides a good assessment of both the local and larger-scale heterogeneities present in this complex system.