The foot-and-mouth epidemic in Great Britain: Pattern of spread and impact of interventions

Science

Volumn 292, Issue 5519, 2001, Pages 1155-1160

  Ferguson, Neil M ^a   Donnelly, Christl A ^a   Anderson, Roy M ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

DRUG INTERACTIONS; MATHEMATICAL MODELS; VACCINES; VIRUSES;

DISEASE TRANSMISSION; FOOT-AND-MOUTH EPIDEMIC;

DISEASES;

ARTICLE; EPIDEMIC; FOOT AND MOUTH DISEASE; INFECTION CONTROL; MATHEMATICAL MODEL; PRIORITY JOURNAL; UNITED KINGDOM; VACCINATION; VIRUS TRANSMISSION;

ANIMALS; ANIMALS, DOMESTIC; APHTHOVIRUS; CATTLE; COMMERCE; DISEASE RESERVOIRS; FOOT-AND-MOUTH DISEASE; GREAT BRITAIN; INCIDENCE; MODELS, BIOLOGICAL; QUARANTINE; SHEEP; SWINE; TIME FACTORS; VACCINATION;

ANIMALIA;

EID: 0035843902     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.1061020     Document Type: Article

References (21)

1. See the British Ministry of Agriculture, Fisheries and Food Web site at www.maff.gov.uk/.
2. J. Gloster, R. M. Blackall, R. F. Sellers, A. Donaldson, Vet. Rec. 108, 370 (1981).
3. M. E. Hugh-Jones, P. B. Wright, J. Hyg. 68, 253 (1970).
4. A. I. Donaldson, T. R. Doel, Vet. Rec. 131, 114 (1992).
5. T. R. Doel, L. Williamson, P. V. Barnett, Vaccine 12, 592 (1994).
6. S. J. Cox et al., Vaccine 17, 1858 (1999).
7. J. S. Salt et al., Vaccine 16, 746 (1998).
8. M. E. J. Woolhouse, A. Donaldson, Nature 410, 515 (2001).
9. 1(r) to the distribution of distances r between identified infectious contacts.
10. R. M. Anderson, R. M. May, Infectious Diseases of Humans (Oxford Univ. Press, 1991).
11. O was estimated from contact data by multiplying the average number of infectious days by the average number of farms infected per infectious day, correcting for the proportion of farms for which no source of infection was identified. We assumed constant infectiousness from 3 days after infection until slaughter (for an average of eight infectious days).
12. 2 - 2rr′cos(θ)
13. S. C. Howard, C. A. Donnelly, Res. Vet. Sci. 69, 189 (2000).
14. D. T. Haydon, M. E. J. Woolhouse, R. P. Kitching, IMA J. Math. Appl. Med. Bio. 14, 1 (1997).
15. 1 times greater than before reporting. The model is novel in tracking not only the numbers of farms in each infection state through time, but also the numbers of pairs of farms connected on the contact network used to represent spatially localized disease transmission. For conciseness and clarity, we only present those for a simpler model with only two infected classes: E (uninfectious) and I (infectious). Using [X] to represent the mean number in state X, [XY] to represent the mean number of pairs of type XY, and [XYZ] to represent the mean number of triples, the dynamics can be represented by the following set of differential equations: d[S]/ dt = -(τ + μ + ω)[SI] - ρβ[S][I]/N, d[E]/dt = ρβ[S][I]/N + τ[SI] - ν[E] - μ[EI], d[I]/dt = ν[E] - s[I] -μ[II], d[SS]/dt = -2(τ + μ + ω)[SSI] - 2ρβ[SS][I]/N, d[SE]/dt = τ([SSI] - [ISE]) - μ([SEI] + [ISE]) - ω)[ISE] + ρβ([SS] - [SE])[I]/N, d[SI]/dt = ν[SE] - (τ + μ + ω)([ISI] + [SI]) - ρβ[SI][I]/N, d[EE]/dt = τ[ISE] -2μ[EEI] - 2ν[EE] + 2ρβ[SE][I]/N, d[EI]/dt = ν[EE] -μ([EI]+[IEI]) - (ν + σ)[EI] + ρβ[SI][I]/N, d[II]/dt = 2ν[EI] - 2σ[II] - 2μ([II] + [III]). The numbers of triples are calculated with the closure approximation (16) [XYZ] ≈ (n - 1)[XY][YZ](1 - φ + φ N[YY]/n[X][Z])/ n[Y], where n is the mean contact neighborhood size of a farm, φ is the proportion of triples in the network that are triangles, and N is the total number of farms [see (12)]. τ = (1 - ρ)β/n is the transmission rate across a contact, where β is the transmission coefficient of the virus, and ρ is the proportion of contacts that are long-range [see (9)], both of which are estimated separately before and after the movement ban. ν is the rate of transit from the uninfectious to the infectious class, and σ is the rate of transit from the infectious to the removed class, μ is the rate at which farms in the neighborhood of an infected farm are culled in ring culling, and ω is the rate at which farms are vaccinated in ring vaccination. It is assumed that vaccination has no effect on previously infected farms.
16. M. J. Keeling, Proc. R. Soc. London B 266, 859 (1999).
17. 0, whereas the latter serves to significantly reduce the overall scale of the epidemic by stopping second-generation transmission events [hence reducing the effective reproductive number (10)].
18. Northumberland Report: The Report of the Committee of Inquiry on Food and Mouth Disease (Her Majesty's Stationery Office, London, 1968).
19. June 2000 Agricultural and Horticultural Census, Ministry of Agriculture, Fisheries and Food, National Assembly for Wales Agriculture Department and Scottish Executive Rural Affairs Department; Crown copyright, 2001.
20. 1 significantly above 1, though more precise estimation awaits availability of detailed data on all slaughter schemes in operation since 30 March 2001.
21. We are extremely grateful for help in the provision of data and for invaluable advice from J. Wilesmith (Veterinary Laboratory Agency), D. Reynolds (Food Standards Agency and Ministry of Agriculture, Fisheries and Food), and D. Thompson (Ministry of Agriculture, Fisheries and Food) and to the many government epidemiologists and veterinary staff who collected the unique contact tracing data on FMD spread in the current epidemic. In addition, we thank D. King (Office of Science and Technology), B. Grenfell, M. Keeling, M. Woolhouse, and other members of the FMD Official Science Group for stimulating discussions; Sir Robert May and Sir David Cox for valuable advice and discussions; three anonymous referees for comments; and S. Dunstan, S. Riley, and H. Carabin for valuable assistance. N.M.F. thanks the Royal Society and the Howard Hughes Medical Institute for fellowship and research funding support. C.A.D. and R.M.A. thank the Wellcome Trust for research funding.