- 1Summary, 126S
- 2Introduction, 126S
- 2.1UK 2001 epidemic, 126S
- 2.2Biology of foot-and-mouth disease, 126S
- 2.3Mathematical models, 127S
- 3Model Development, 127S
- 3.1Data, 127S
- 3.2Branching process model, 127S
- 3.3Other models, 128S
- 4Monte Carlo simulation model, 128S
- 4.1Model structure and inputs, 128S
- 4.2Model output, 128S
- 4.3Scenario modelling, 129S
- 5Vaccination, 129S
- 5.1Properties of vaccines, 129S
- 5.2Modelling vaccination, 129S
- 6Conclusions, 129S
- 7Acknowledgements, 130S
- 8References, 130S
Mathematical models were used to guide the UK foot-and-mouth disease (FMD) control policy during the 2001 epidemic. Based on data collected during the epidemic, prospective modelling using a variety of approaches gave the same conclusions: (i) that the epidemic had not been brought under control by ‘traditional’ methods, and (ii) that neighbourhood control measures (the contiguous cull) could bring the epidemic under control and result in a net saving of livestock. Retrospective analyses suggest that the subsequent course of the epidemic was consistent with a beneficial impact of the contiguous cull and that it would have been difficult to achieve a better outcome using reactive vaccination, which would have required very large-scale vaccination programmes to have been implemented quickly. Perhaps the most important lesson to be learned is the vital importance of rapid and decisive intervention in response to an outbreak, including the earliest possible implementation of a national ban on the movement of livestock once the presence of disease is confirmed.
2.1 UK 2001 epidemic
Foot-and-mouth disease was confirmed in the UK on 20 February 2001. Retrospectively, by that date there were at least 30 (and, according to some estimates, over 50) incubating cases, widely disseminated from south-west Scotland to Devon, largely through extensive movements of sheep through sheep markets from a focus around the putative index case in Northumberland. By 23 February, when a national ban was imposed on livestock movements, the number of incubating cases had approximately doubled. The large number and wide distribution of cases made this epidemic particularly difficult to control; for example, by 23 Februrary there were already many millions of animals at risk, many more than the number of vaccine doses immediately available. Ultimately, there were over 2000 cases and the epidemic lasted until the end of September 2001. Over one million livestock were slaughtered on infected holdings, a further three million (mostly sheep) were slaughtered for disease control purposes, and a further two and a half million were slaughtered for welfare reasons. The total cost has been put at £3 billion directly and a further £5 billion indirectly (National Audit Office 2002).
2.2 Biology of foot-and-mouth disease
The FMD is caused by a single-stranded RNA virus (FMDV, a member of the Picornaviridae family). There are seven different serotypes; the UK epidemic was caused by the Pan-Asian strain of type O FMDV. The disease has a near global distribution but is no longer endemic in Europe. It is highly infectious: an infected pig can produce up to 1012 virions per day. It has a variety of transmission routes, including animal-to-animal contact, contamination of the environment and air-borne spread. The incubation (latent) and infectious periods are short, often just a few days. Clinical signs are variable but the disease can cause significant losses of production and some mortality, and FMD is one of the livestock diseases on the Office International des Épizooties (OIE) List A (http://www.oie.int).
The effectiveness or otherwise of any FMD control programme is intimately related to the transmission biology of the FMD virus. There are two key points. First, the course of infection on a farm is extremely fast; the interval between exposure and slaughter was typically only about 10 days in the UK. Secondly, infected animals can transmit virus before clinical signs appear and disease is reported, and only a few days of transmission may be enough to sustain an epidemic. In the UK, transmission rates were so high, with 75% of transmissions occurring up to and including the day of reporting, that culling infected holdings alone was insufficient to bring this particular epidemic under control.
2.3 Mathematical models
Mathematical models have been widely used in epidemiology, but have had very little influence on the design and operation of control programmes for FMD, with the exception of models designed to trace the movements of plumes of airborne virus (Sorensen et al. 2000). However, mathematical models have been used in the interpretation both of FMD outbreaks in individual herds or flocks (Hutber and Kitching 2001) and of larger epidemics (Haydon et al. 1997; Howard and Donnelly 2000) and these applications have provided guidance regarding control options, including the importance of rapid intervention and the advantages and disadvantages of culling and vaccination as control options.
3. Model Development
The data available for analysis included: the location of all reported infected premises (IP), as a grid reference; the numbers and species of livestock on the premises; the date of reporting; the date of slaughter (stamping out); results of laboratory diagnostic testing; the estimated date of infection (based on ageing of lesions and possible dates of exposure from epidemiological tracings); and, for some IPs, the possible origin of infection (based on epidemiological tracings). In addition, census data provided information on the locations of and the numbers and species of livestock on the great majority of farm holdings in the UK, and records were available of the dates of culling out of at-risk premises [initially just dangerous contacts (DC)] as part of the control effort. Potential problems with these data included: dates of infection were estimates only and may have been biased, especially in sheep flocks where clinical signs may be difficult to detect and disease may have been present longer than supposed; epidemiological tracings must often be determined on a balance of probabilities; census data did not necessarily correspond with the situation on farm several months after the census; grid references were inconsistent with postal addresses for a small percentage of holdings, and referred to farm house rather than livestock; information on the culling of at-risk premises sometimes became available only after considerable delay; and in a significant minority of cases there were inconsistencies between clinical and laboratory diagnosis (although it is not yet known to what extent these reflect poor specificity of clinical diagnosis or poor sensitivity of laboratory testing – which is based on a combination of antigen enzyme-linked immunosorbent assay (ELISA), antibody ELISA and tissue culture – when applied to field collected material).
Despite these deficiencies the dominant patterns of the epidemic were obvious and robust and the model projections based upon these patterns were of predictive value (see below). However, an understanding of dynamics of the global epidemic is not a substitute for local decision making, which is essential to validate centrally-managed databases against the true situation on the ground.
Two key observations were that FMD was out of control in the UK during mid-March (in a formal sense defined below) and that in many cases the disease was spreading locally. The importance of local spread is illustrated by data collected during the period when the majority of contiguous premises (CP), were being removed as part of the control effort. Even then, over half of all new cases arose within 1·5 km of a previously reported case, or within 2·5 km of a case reported in the previous 7 days. Similarly, tracing studies indicated that at least 50% of transmissions took place over distances <3 km. There is no evidence that this spread was caused by aerosol transmission (Donaldson et al. 2001) and, in most cases, the actual mechanism of spread remains uncertain (Gibbens et al. 2001). However, it is clear that local spread was an important factor during this epidemic.
3.2 Branching process model
Contact tracing data supplemented by estimation of most probable source of infection as a function of distance allows calculation of the case reproduction ratio, R, the average number of new cases per case (Woolhouse et al. 2001). In mid-March the best estimate of R was 1·45 (95% CI +0·10) (Haydon et al. 2003). The distribution of R values was highly overdispersed, with 40% cases responsible for 80% new cases and approximately one-third of cases not associated with any new cases at all.
To make a short term projection of the increase in reported numbers of cases requires an estimate of R and three other variables: (i) I, the number of current infections, (ii) the generation time, G, the mean interval between the date of infection of a holding and the dates of infection of holdings infected from it, and (iii) T, the interval between infection and reporting. I was originally estimated by back-calculation, but can now be obtained retrospectively using estimated dates of infection. G was estimated from tracing and date of infection data and had a mean of 7·0 days with a wide distribution. T was estimated from dates of infection and reporting and had a mean of 8·2 days, also with a wide distribution (Haydon et al. 2003).
The distributions of R, G and T reflected the many heterogeneities between holdings, including different incubation times and speed of reporting in different livestock species, and different susceptibilities and infectiousnesses of different livestock species and farm types.
Using data up to 15 March only, estimates of these variables allowed stochastic projections, which gave the central prediction that the epidemic would double in size within the next 7–9 days. This prediction was in agreement with subsequent observation up to 24 March, consistent with the notion that the disease was out of control at that time. However, projections of this kind are suitable only for the early, ‘exponential’ phase of an epidemic and break down once local depletion of susceptible animals becomes important.
3.3 Other models
The other modelling approaches used were: (i) spatially explicit microsimulation model – Interspread (Morris et al. 2001), (ii) a mass action model using moment closure to approximate neighbourhood effects (Ferguson et al. 2001a), and (iii) a spatially explicit Monte Carlo simulation model (Keeling et al. 2001) – see Section 4.1.
All four models agreed on three key conclusions: (i) the epidemic was ‘out of control’ in the sense of R > 1 (see Section 2.2); ii) the ‘traditional’ control methods of stamping out IPs and tracing and stamping out DCs were unlikely to be sufficient to reduce R < 1 quickly, even if IP culling was achieved within 24 h, and (iii) that neighbourhood control policies, i.e. preventive slaughter on holdings in the neighbourhood of IP, would reduce R < 1 and would result in a net saving of livestock. The latter conclusion influenced the adoption by the UK government of the CP cull as part of its FMD control strategy. The revised culling strategy was referred to as 24/48: IPs to be culled within 24 h, and DCs and CPs within 48 h.
4. Monte Carlo Simulation Model
4.1 Model structure and inputs
The model developed by Keeling et al. (2001) has the structure:
where: Pi is the probability that susceptible farm i is infected on day t; S and T are vectors of susceptibility and transmissibility by species respectively; Ni is the species* numbers vector for farm i; K(dij) is the relative rate of infection as a function of distance separating farms i and j, dij; j ∈ It) is the set of extant farms on day t infected five or more days previously.
Four parameters must be estimated from the data: three of the species-specific susceptibilities and transmissibilities (given that only cattle and sheep played a major role in the epidemic); and the fraction of DCs that were incubating infection. The model therefore reflects the main risk factors for the spread of FMD at the farm level: distance from potential sources of infection (the most important factor); livestock species; and numbers of livestock on the farm. Large cattle farms in high livestock density areas were therefore at greater risk than small sheep farms in low livestock density areas.
The model has three external inputs: (i) the distribution of livestock on all livestock holdings in Britain, (ii) the initial distribution of infected holdings at the time of the national livestock movement ban on 23 February , and (iii) observed culling effort, both of IPs and of at-risk premises (as distinct from culling targets, which were often not met). Full details of model structure and parameterization are given in Keeling et al. (2001).
4.2 Model output
The model reproduces the observed time course of the UK epidemic satisfactorily, with the observed epidemic falling well within the range of stochastic variation generated by the model (Keeling et al. 2001). In particular, the model reproduces the observed peak of reported cases in late March, shortly after the introduction of the extended cull (including culling of some premises within 3 km of an IP in certain regions). Two effects are important here: (i) a reduction in transmission rates, not seen until at least one disease generation (ca. 7 days) later; and (ii) an immediate effect because of the removal of incubating premises which would otherwise have been reported (Woolhouse et al. 2001). This demonstrates that the observed course of the epidemic was consistent with the expected impact of the 24/48 strategy (but does not preclude other interpretations of the same data). At a finer scale, similar effects were seen within the most affected regions – Cumbria, Dumfries and Galloway and Devon – with differences in timings of the epidemic peak consistent with differences of timings in the implementation of the extended cull. The model also reproduces the long epidemic tail, which is at least partly because of the pattern of spatial spread during that stage and is difficult to reproduce without a spatially explicit model (cf Ferguson et al. 2001b).
The model also reproduces the observed spatial distribution of cases, with most cases confined to hotspots in Cumbria, Dumfries and Galloway, Devon, north-east England and mid Wales, and sporadic cases or small clusters of cases elsewhere. At a finer scale the model reproduces the observed clustering of cases within <3 km of previous cases.
4.3 Scenario modelling
The model can be used to explore the expected impact of alternative control strategies. One possible strategy is the rigorous implementation of traditional control measures, at the highest levels ever achieved during the UK epidemic, combined with implementation of the national movement ban on 20 February (when the presence of disease was confirmed) rather than 23 February. On average, this results in a significant reduction in numbers of cases, the number of premises culled, and the total number of livestock lost as a direct consequence of the control programme. However, a substantial epidemic still results and the outcome is sufficiently variable, as a result of stochastic effects, that there is a significant probability of a worse outcome than was actually observed.
A second scenario is to supplement traditional measures with a CP cull, implemented from 20 February. On average, this results in a much greater reduction – close to 90%– of the number of cases, the number of premises culled, and the total number of livestock lost. Although there is variation around the mean, this is clearly the preferred strategy. In practice, the CP cull was not introduced until a month into the epidemic. Even so, the best estimate is that the policy resulted in a net saving of at least 0·5–1·0 million livestock (Keeling et al. 2001; Matthews, pers. comm).
5.1 Properties of vaccines
Three properties of FMD vaccines (and, to varying degrees, all vaccines) can compromise their ability to control the spread of infection. First, the vaccines do not provide 100% protection; typical efficacies for FMD vaccines are in the range 90–95% (Barnett and Carabin 2002). Secondly, FMD vaccines do not provide immediate protection; high potency vaccines may protect within 3–4 days, standard vaccines take considerably longer (Barnett and Carabin 2002). Thirdly, vaccination has no or limited effect on animals which are already infected. Because of these properties, although vaccination can prevent transmission of FMD at the population level it does not do so immediately and substantial outbreaks or epidemics can still occur. An example of this comes from Saudi Arabian cattle farms where outbreaks continued to occur despite a combined prophylactic and reactive vaccination programme (Woolhouse et al. 1996). Another example comes from Uruguay and Argentina where major epidemics occurred in 2001 despite the early implementation of mass reactive vaccination campaigns covering tens of millions of animals.
5.2 Modelling vaccination
Various reactive vaccination scenarios can be explored using the above model (Keeling et al. 2001, 2003). These studies suggest several general conclusions. First, reactive vaccination must be implemented on an appropriate geographical scale; in the case of a disseminated epidemic this will be regional or national – small scale ring vaccination may have limited impact. Secondly, reactive vaccination (as with any other FMD control measure) must be implemented quickly. To achieve this it is clearly necessary to have the logistic capacity to deliver very large numbers of immunizations (possibly hundreds of thousands per day). Finally, one possible strategy is to use vaccination as a complement to, rather than a replacement of, the culling of at-risk holdings, as in the Netherlands in 2001. For this strategy to be effective, it is important that implementation of the vaccination programme does not reduce the resources available to the culling programme, nor lower compliance with the culling programme.
There are many lessons to be learned, both scientific and operational, from the UK 2001 epidemic. These are discussed in detail elsewhere (Royal Society 2002), but some key issues are as follows:
- – better contingency planning based on wide consultation, peer-reviewed and agreed with stakeholders;
- – rapid and decisive intervention in response to an outbreak;
- – immediate imposition of a national ban on livestock movements as soon as disseminated disease is suspected;
- – rapid slaughter of livestock on infected premises;
- – if control is to be achieved by slaughter of at-risk premises then this needs to be better targeted at high risk premises in the neighbourhood of a case, not just those deemed ‘contiguous’;
- – if control is to be by reactive vaccination then this needs to be implemented quickly at appropriate spatial scale and the necessary resources have to be available to achieve this;
- – prioritization of research into better diagnostics (both more specific clinical diagnosis and rapid, sensitive tests for preclinical FMD), better vaccines (giving higher levels of protection, achieved more quickly, and blocking transmission from vaccinated animals) and better mathematical models to guide decision-making.
I am grateful to my colleagues Darren Shaw, Margo Chase-Topping, Lousie Matthews, Dan Haydon, Suzanne St Rose, Bryan Grenfell and Matt Keeling for their contributions to this work, and to colleagues at the Institute for Animal Health and the Veterinary Laboratories Agency.