ScienceDirect - Research in Veterinary Science : Mathematical modelli he foot and mouth disease epidemic of 2001: strengths and weaknesses

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1 Login: Register Home Browse Search My Settings Alerts Help Quick Search All fields Author Journal/book title Volume Issue Page Advanced Search Research in Veterinary Science Volume 73, Issue 3, December 2002, Pages Font Size: Find more full-text articles: Your search for "foot mouth uk 2001 modeling ferguson " would return 147 results on ScienceDirect. View Results Article Figures/Tables References PDF (105 K) Thumbnails Full-Size Images doi: /s (02) Article Toolbox Copyright 2002 Published by Elsevier Science Ltd. Review Mathematical modelling of the foot and mouth disease epidemic of 2001: strengths and weaknesses Article Cited By Save as Citation Alert Citation Feed Export Citation Add to my Quick Links Cited By in Scopus (20) L. E. Green and G. F. Medley, Ecology and Epidemiology Group, Department of Biological Sciences, University of Warwick, Coventry CV4 7AL, UK Available online 14 November Article Outline Understanding mathematical models Types of modelling Mathematical model validity Design of control policies Mathematical models in control of FMDV References IN 2001 an epidemic of foot and mouth disease (FMD) occurred in the UK. This was the first large outbreak since 1967, when 2364 farms were infected. The disease was diagnosed and confirmed on 20th February 2001 and a ban on the movement of livestock was introduced three days later. Investigations indicate that the first affected farm was infected approximately days before 20th February. As a consequence of the delay in identification of diseased animals and the delay in preventing movement of all livestock after confirmation that the foot and mouth disease virus (FMDV) was present in the UK, 70 farms throughout England were infected on the day that control measures were introduced. A detailed description of the further spread and control of FMDV can be read in Gibbens et al (2001). Related Articles in ScienceDirect DISEASES OF DAIRY ANIMALS, INFECTIOUS Foot-and- Mouth... Encyclopedia of Dairy Sciences Epidemiological inference for partially observed epidem... Epidemics Foot-and-Mouth Disease Vaccines for Biodefense and Emerging and Neglected Dise... A point pattern model of the spread of foot-and-mouth d... Preventive Veterinary Medicine Application of non-structural protein antibody tests in... Vaccine View More Related Articles View Record in Scopus Mathematical modelling was used to guide policy decisions on the control of FMD through regular meetings with the science group. This is the first time that this type of modelling has been used for FMD control in the UK and, to our knowledge, in the rest of the world. However, similar techniques have been used more widely as a tool to aid in the design of control programmes against infectious disease. For example, a highly topical issue is the current debate about the use of MMR (measles, mumps & rubella) vaccine. The target coverage for MMR vaccination is 95%. This figure is derived from mathematical models of infection transmission that estimate that in order to Page 1 of 7

2 prevent a measles epidemic it is estimated that more than 95% of the population must be immune (ideally by vaccination) (Anderson & May 1990; Farrington et al 2001). The purpose of this review is to present the basis of mathematical modelling and its strengths and weaknesses when used in a situation such as the FMDV epidemic, i.e., to make strategic decisions rapidly. For reviews of other applications see De Jong (1995) and Woolhouse et al (1997). Understanding mathematical models One aspect should be made clear at the start. The mathematical models are of infection (i.e., FMDV) rather than disease (FMD). Consequently, they are designed to mimic the spread of infection rather than disease. It is the process of infection that is key, rather than disease, which is dependent on many additional factors. Mathematical modelling describes the dynamics of infection through time and/or space. At its simplest, classes of infection status are used to define a set of mutually exclusive states that an individual can have. Such classes can include susceptible, infected, infectious and immune (see Fig 1). In the case of this epidemic, an individual refers to an individual farm or property, but more usually it is individual animals that are used as the basic unit in the infection process. Clearly these classes are not always used in every infection process, e.g., as far as we are aware Johne's disease does not have an immune' state after being infectious' and sometimes other classes are necessary, e.g., bovine viral diarrhoea (BVD) almost certainly has a carrier' state. FIG 1. Full-size image (5K) Spread of infection is dependent upon the presence of susceptible animals: if all animals are immune (either through natural infection or vaccination) then there is no susceptible pool and there can be no infection or disease. We presume that all UK livestock were susceptible to FMDV before 1st January Lack of infection and disease was dependent upon lack of exposure of livestock to FMDV, ensured through legislation. The dynamic process of modelling occurs because individuals move between classes at a certain rate (indicated by arrows on Fig 1), e.g., pigs move from infected and incubating to infected and diseased with FMDV at a rate of 0.25/pig/day (assuming an average incubation period of 4 days). The information for these rates usually comes from published literature or experimental infection studies done specifically to answer these questions. The most influential process is that of infection. The risk that a susceptible farm becomes infected is dependent upon its rate of exposure to the pathogen. This is determined by the contact rate (between farms), which is influenced by moving and mixing of animals and animal products (both susceptible and infected), e.g., infected animals or contaminated lorries or feed, and the probability that this contact is successful. For example, exposure to another animal may give a greater probability of infection than exposure to a contaminated lorry. The total rate of infection in the population is dependent upon both the numbers of susceptible and infected farms, so that the infection rate is zero either when no farms are infectious or when no farms are susceptible. An epidemic occurs when the rate of transition of farms from susceptible to infected is greater than the rate at which they become immune. Then the number of infected and infectious increases (and that increase fuels a further increase in the infection rate) and there is an epidemic. The epidemic peaks and falls when the number of susceptibles becomes so low that the rate of infection falls below the rate at which farms are recovering or being removed (culled). Page 2 of 7

3 Where all farms are susceptible to disease then the introduction of the pathogen will lead to an epidemic if the product of the contact rate and the probability of a successful transmission of pathogen is above a threshold. This is R 0, the basic reproductive number or ratio. For the FMDV epidemic, R 0 was defined as the average number of farms infected by one farm in a totally susceptible population of farms. When FMDV was uncontrolled at the start of the epidemic it was estimated that each affected farm infected 23 farms (Woolhouse et al 2001), i.e., R 0 =23. As an epidemic naturally progresses, and a decreasing number of farms remain susceptible, the average number of farms that each farm infects will fall (because potential infection events will be between farms already infected). Consequently, the effective reproductive number, R, becomes the more important measurement. The aim of all control programmes is to reduce R to below one, so that on average each infected farm infects less than one other farm. Types of modelling The modelling described above is deterministic modelling. In this case, a simple model is used to describe average effects and the rates of flow through the system are, again, averages. As the name model suggests, it is a simplification of a much more complex system, and the level of simplification is an art as well as a science. For example, none of the models used for FMDV included any weather variables, despite evidence that FMDV can be transmitted by wind. This is essentially because the time taken to include meteorological data, and so complicate the model enormously, was not thought likely to improve the model predictions. To include an additional parameter in a model there must be good evidence that the increase in complexity will improve model predictions and it is vitally important to have good quality data available. It may be that within a multidisciplinary team advice is given that a further complexity is necessary and important. For example, the initial models of FMDV did not use species differences but considered one infection rate for all livestock. However, further investigation, and disagreement about this assumption led to its inclusion in later models. Deterministic modelling was used by Ferguson and Ferguson for the FMDV epidemic in the UK in These models are of limited use to predict a quantified outcome in one outbreak since any one epidemic does not follow an average pattern: it is a one off'. The main purpose of deterministic models is to aid understanding and to increase knowledge. Such models frequently raise hypotheses for further investigation of host pathogen relationships. They have been used successfully to develop understanding of virtually all diseases: human, animal and plant ( Anderson and May 1990). In contrast to deterministic models, stochastic models contain and produce variability. In the FMDV models this variability comes from two main sources. The first is that the likelihood and timing of events is a random process. For example one farm may potentially act as the source of infection for another farm, but not all farms challenged with FMDV become infected and when they do, the time when infection occurs is largely unpredictable. The second source concerns the fact that farms (and their animals) come in whole numbers. A deterministic model might predict that 67.4 farms are infected, but a stochastic model will predict that there is a 5% chance of 65 farms being infected, a 25% chance of 66 farms, etc. In other words, stochastic models give a range of behaviours or patterns rather than one average pattern. There is a probability distribution around each mean rate of change, so that rather than define the rate of incubation as 0.25/pig/day it may be defined as /pig/day, i.e., incubation lasts from days. The probability of each of these incubation periods can be modelled to form a distribution that peaks at 4 days. This variability provides a range of effects, i.e., a confidence interval between which the likely course of epidemic will probably lie. Such models were used by Keeling et al (2001) and Woolhouse et al (2001) in the 2001 FMD epidemic in the UK. These models also allow extinction: when the epidemic is decreasing there is a probability that at a point in time no farms will become infected. This does not occur in deterministic modelling, in this situation the average' infection level would be very low, e.g., farms infected. The final complexity of the FMDV epidemic was that the pattern of spread was through both time and space. There are established techniques for modelling through time and identifying correlations between events, but this is more difficult through space and highly complex through space and time. A simplified mathematical technique for modelling epidemics in time and space Page 3 of 7

4 was first proposed by Keeling (1999) and used by Ferguson and Ferguson in the recent epidemic. Whilst Morris et al (2001) and Keeling et al (2001) modelled individual farms with explicitly spatial models. Again the level of complexity of spatial modelling is an art and introducing factors such as physical geography is not a small task. Modern weather forecasting has essentially the same problem, although somewhat more complex because air can move in three dimensions. However, weather forecasters have a considerable advantage because of their access to vast quantities of accurate data from satellite, weather stations, radar and the like. Likewise, the modellers needed detailed and accurate data on the spatial distribution of farms and livestock, and the current epidemic situation. Unfortunately, these data were not always reliable or known. This created a serious problem for predictions from these models. It is like asking a forecaster what the weather will be tomorrow, without providing information on both the weather today and the position in the world to be forecast. For an example of the interaction between models and data in the design of vaccination programmes against human viral infections see the following papers: de Serres et al (2000), Gay et al (2000), Osborne et al (2000), Farrington et al (2001). Mathematical model validity The use of mathematical models to predict epidemic processes, and to relate them to data is not an exact science (Donnelly & Ferguson, 2000), even if very good data exist ( Medley 2001). Consequently, proof of the accuracy or validity of any model should be required before it is used to influence policy. There are techniques to test the validity of a model to describe a system. The most important aspect is that a valid model should be true for data not used in the modelling process and, in fact when developing models for research, the final stage is to compare them with data not used at all in model development. A second is that the model should not be considered complete until sensitivity analysis is used to identify the rates that have a large impact on the modelling process. It is important that sensitive rates are estimated correctly; if the data for these rates are poor, then more data are required. Sensitivity analysis was used to identify important rates of change in the FMDV models. One further technique that is underused and may have been of help in establishing the robustness of the FMD models is identifiability. This technique tests whether the predicted curve of the model could have more than one solution for a given set of parameters, i.e., could one have the same curve with different rates between each state. It has been used in modelling of mastitis in dairy cows (White et al 2001) and may have given more credibility to the modelling of FMDV when all data up to the beginning of May were used in the models. However, it is not a simple procedure (especially in models with the complexity of those developed for FMDV), and lack of time would have prevented a full analysis of these models. Design of control policies It has been said that all models are wrong, but some models are useful (George Box). But how wrong does a model have to be before it is useless and how useful does it have to be before policy can be built on it? The principal use of mathematical models in infectious disease control is to ask what-if questions. What happens if we cull all animals within 3 km of a case? What happens if we cull 50% of animals within a 6 km radius? What happens if we cull all animals on farms with more than 50 livestock within a 10 km radius? Such questions can be answered (under the model assumptions) at relatively very little cost (a fast computer, a salary, a talent and a good education) if they are asked. The options for control that result from using mathematical models are not hampered by logistic, economic, or political considerations. However, the quantitative results themselves are not particularly relevant, rather it is the understanding that this research produces which is most informative. Such an insight might be that if the radius of any cull is less than the mean radius of infection spread, then culling will have very little effect, since it will always be chasing the epidemic. Often, these insights appear obvious' once they have been described. More useful questions are those that include a cost, such as, which control policy will eliminate Page 4 of 7

5 FMDV and minimise the numbers of animals killed? Or minimise the economic cost (e.g., Vonk Noordegraaf et al 1998). Such models always indicate that the earlier infection is controlled, the cheaper the control will eventually be. It is therefore highly likely to be cost-beneficial to pay to be prepared to control epidemics such as FMDV immediately, since a delay of only a few days in initiating control can increase the overall cost substantially. Again, these predictions are not hampered by political constraints, and, again, it is the understanding gained that is most important. Mathematical models in control of FMDV However, in the specific case of this epidemic, modelling was asked a completely different question: what should we do next? The difference here is not so much in terms of the actual calculations that have to be performed, but in the quality of data required, the knowledge of the FMD virus in the UK in 2001, the host pathogen environment interactions that were occurring in the UK in 2001 and what was logistically feasible and acceptable. The what if?' and cost' questions can be asked and answered generically, i.e., the actual situation is not really an issue it is the underlying mechanism that is being sought. Imagine you are asked why cars stop on motorways, and you discover that running out of petrol is the most likely (generic) answer. Then you are asked why this particular car has stopped on the motorway. Now, because you have a generic understanding of the problem, the first thing you are likely to do is try and find out whether the car has petrol in it. In the same way, a generic answer to control of FMDV is to prevent susceptible animals contacting FMDV by stopping all movements that could result in exposure to the virus and by removing infectious animals. The control policies tested were those based on minimising transmission as quickly and as reliably as possible. This can be done by removing susceptible animals (killing, vaccinating or quarantine) and/or infectious animals (killing or quarantine) the basic requirements for control of all infectious diseases. The key to successful control is to get the effective reproduction number, R, below 1 (Grenfell and Woolhouse 2001). Consequently, there was considerable attention given to this one parameter. Having decided that vaccination was not an option ( Woolhouse and Donaldson 2001), the role of the modelling was to determine which culling policy would bring the epidemic under control (i.e., reduce R below 1) as quickly as possible. Therefore a final problem, and by no means the least, is that the answers to what should we do next?' were required within a very short time. There is also a more philosophical problem concerning predictability. Models such as those developed for FMDV have been shown to be predictive (e.g., Grenfell et al 2002), but only in situations where there is no control operating, clearly not the case in the models for FMDV. To assess their predictive accuracy we need more epidemics where FMDV has occurred in similar situations or we need situations where the outbreak was similar but modelling was not used. All three models developed produced similar conclusions. They described the change in the epidemic each week and indicated whether FMDV was increasing (R>1) or decreasing (R<1). The scientists involved also checked that policies had been adopted, e.g., were livestock on contiguous premises being culled. A total of 2026 premises were infected with FMDV in the 2001 epidemic, a similar number to the 1967 outbreak, which started when contaminated meat was fed to pigs from several farms. This was therefore a multi point-source exposure. However, in 1967 the infected farms were detected rapidly (4 days) and were all within a small geographical location whereas in 2001 the point source exposure spread from one farm was not detected for days by which time there were infected premises in many geographical areas. This simple comparison suggests that the attempts to control FMDV were more successful than in 1967, which may, in part, be due to the insight gained from the modelling. However, a more detailed comparison, including costs such as the numbers of animals culled/farms depopulated, is clearly required. Major efforts are and should now be targeted at using the 2001 data to test the what if?' and cost?' questions. Whilst the data are from only one outbreak the information from these more detailed and time consuming analyses will be invaluable in understanding and controlling future outbreaks. The risk of another outbreak of FMDV, or another exotic pathogen, can never be zero whilst UK livestock remain susceptible. Economics, logistics, knowledge, and politics all drive policy and mathematical modelling can be a tool that when used with wisdom, within a strong multidisciplinary forum, can usefully assist in making policy decisions. Page 5 of 7

6 References Anderson and May, R.M. Anderson and R.M. May, Infectious Diseases of Humans: Dynamics and Control., Oxford University Press, Oxford (1990). De Jong, M.C.M. De Jong, Mathematical modelling in veterinary epidemiology: why model building is important. Prev. Vet. Med (1995), pp Abstract PDF (775 K) de Serres et al, G. de Serres, N.J. Gay and C.P. Farrington, Epidemiology of transmissible diseases after elimination. Am J Epi 151 (2000), pp View Record in Scopus Cited By in Scopus (53) Donnelly and Ferguson, C.A. Donnelly and N.M. Ferguson In: Statistical Aspects of BSE and CJD: Models for Epidemics, Chapman and Hall, London (2000). Farrington et al, C.P. Farrington, M.N. Kanaan and N.J. Gay, Estimation of the basic reproduction number for infectious diseases from age-stratified serological survey data. Applied Statistics 50 (2001), pp Ferguson et al, 2001a. N.M. Ferguson, C.A. Donnelly and R.M. Anderson, The foot-and-mouth epidemic in Great Britain: pattern of spread and impact of interventions. Science 292 (2001a), pp Full Text via CrossRef View Record in Scopus Cited By in Scopus (175) Ferguson et al, 2001b. N.M. Ferguson, C.A. Donnelly and R.M. Anderson, Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain. Nature 413 (2001b), pp Gibbens et al, J.C. Gibbens, C.E. Sharpe, J.W. Wilesmith, L.M. Mansley, E. Michalopoulou, J.B.M. Ryan and M. Hudson, Descriptive epidemiology of the 2001 foot-and-mouth disease epidemic in Great Britain: the first five months. Vet. Record 149 (2001), pp View Record in Scopus Cited By in Scopus (94) Grenfell et al, B.T. Grenfell, O.N. Bjornstad and B.F. Finkenstadt, Endemic and epidemic dynamics of measles. II. Scaling noise, determinism and predictability with the time series SIR model. Ecological Monographs 72 2 (2002), pp Full Text via CrossRef View Record in Scopus Cited By in Scopus (42) Grenfell and Woolhouse, B.T. Grenfell and M.E.J. Woolhouse, Managing foot-and-mouth. Nature 410 (2001), pp Gay et al, N.J. Gay, L. Hesketh, P. Morgan-Capner and E. Miller, Ten years of serological surveillance in England and Wales: methods, results, implications and action. International Journal of Epidemiology 29 (2000), pp Keeling, M.J. Keeling, The effects of local spatial structure on epidemiological invasions. Proc. Roy. Soc. B266 (1999), pp Keeling et al, M.J. Keeling, M.E.J. Woolhouse, D.J. Shaw, L. Matthews, M. Chase-Topping, D.T. Haydon, S.J. Cornell, J. Kappey, J. Wilesmith and B.T. Grenfell, Dynamics of 2001 the foot and mouth epidemic: stochastic dispersal and a heterogenous landscape. Science 294 (2001), pp Full Text via CrossRef View Record in Scopus Cited By in Scopus (196) Medley, G.F. Medley, Predicting the Unpredictable (Perspective). Science 294 (2001), pp Full Text via CrossRef View Record in Scopus Cited By in Scopus (15) Morris et al, R.S. Morris, J.W. Wilesmith, M.W. Stern, R.L. Sanson, M.A. Stevenson and K. Osborne, Predictive spatial modelling of alternative control strategies for the foot-and-mouth disease epidemic in Great Britain Vet Record 149 (2001), pp View Record in Scopus Cited By in Scopus (71) Osborne et al, K. Osborne, N.J. Gay, L. Hesketh, P. Morgan-Capner and E. Miller, Ten years of serological surveillance in England and Wales: methods, results, implications and action. International Journal of Epidemiology 29 (2000), pp Full Text via CrossRef Page 6 of 7

7 Vonk Noordegraaf et al, A. Vonk Noordegraaf, J.A.A.M. Buijtels, A.A. Dijkhuizen, P. Franken, J.A. Stegeman and J. Verhoeff, An epidemiological and economic simulation model to evaluate the spread and control of infectious bovine rhinotracheitis in the Netherlands. Prev. Vet. Med. 36 (1998), pp Article PDF (199 K) View Record in Scopus Cited By in Scopus (24) White et al, L.J. White, N.D. Evans, T.J.G.M. Lam, Y.H. Schukken, G.F. Medley, K.R. Godfrey and M.J. Chappell, The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in diary cows. Mathematical Biosciences 174 (2001), pp Article PDF (199 K) View Record in Scopus Cited By in Scopus (8) Woolhouse et al, M.E.J. Woolhouse, M. Chase-Topping, D.T. Haydon, J. Friar, L. Matthews, G. Hughes, D.J. Shaw, J. Wilesmith, A. Donaldson, S.J Cornell, M.J. Keeling and B.T. Grenfell, Foot-and-mouth disease under control in UK. Nature 411 (2001), pp Full Text via CrossRef View Record in Scopus Cited By in Scopus (40) Woolhouse et al, M.E.J. Woolhouse, D.T. Haydon and D.A.P. Bundy, The design of veterinary vaccination programmes. Vet. J (1997), pp Abstract PDF (567 K) View Record in Scopus Cited By in Scopus (21) Woolhouse and Donaldson, M. Woolhouse and A. Donaldson, Managing foot-and-mouth. The science of controlling disease outbreaks. Nature 410 (2001), pp Full Text via CrossRef View Record in Scopus Cited By in Scopus (29) Fax: ; graham.medley@warwick.ac.uk Research in Veterinary Science Volume 73, Issue 3, December 2002, Pages Home Browse Search My Settings Alerts Help About ScienceDirect Contact Us Information for Advertisers Terms & Conditions Privacy Policy Copyright 2009 Elsevier B.V. All rights reserved. ScienceDirect is a registered trademark of Elsevier B.V. Page 7 of 7