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. 2005 Dec 6;102(49):17588-93.
doi: 10.1073/pnas.0509003102. Epub 2005 Nov 23.

Simple model for tuberculosis in cattle and badgers

D R Cox  1 , Christl A Donnelly, F John Bourne, George Gettinby, John P McInerney, W Ivan Morrison, Rosie Woodroffe
Affiliations

Simple model for tuberculosis in cattle and badgers

D R Cox et al. Proc Natl Acad Sci U S A. .

Abstract

As an aid to the study of bovine tuberculosis (TB), a simple model has been developed of an epidemic involving two species, cattle and badgers. Each species may infect the other. The proportion of animals affected is assumed relatively small so that the usual nonlinear aspects of epidemic theory are avoided. The model is used to study the long-run and transient effect on cattle of culling badgers and the effect of a period without routine testing for TB, such as occurred during the 2001 epidemic of foot-and-mouth disease in Great Britain. Finally, by examining the changes in cattle TB over the last 15 years, and with some other working assumptions, it is estimated that the net reproduction number of the epidemic is approximately 1.1. The implications for controlling the disease are discussed.

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Figures

Fig. 1.
Fig. 1.
The standardized prevalence of TB in cattle (Eq. 6) as a function of time, τ, since culling; the proportion by which the badger population was reduced, k; the relative cattle-to-cattle transmission rate, l; and a measure of the relative influence of badgers as compared with disease in cattle restocked into the system, IB.
Fig. 2.
Fig. 2.
The standardized incidence of TB in cattle herds (Eq. 7) as a function of time, τ, since culling; the proportion by which the badger population was reduced, k; the relative cattle-to-cattle transmission rate, l; and a measure of the relative influence of badgers as compared with disease in cattle restocked into the system, IB.
Fig. 3.
Fig. 3.
The standardized prevalence of TB in cattle herds (Eq. 11) after a 9-month cessation of testing and restocking as a function of time, τ, since resumption of skin testing and restocking of cattle; the relative cattle-to-cattle transmission rate, l; and a measure of the relative influence of badgers as compared with disease in cattle restocked into the system, IB.
Fig. 4.
Fig. 4.
The number of TB herd incidents each year in Great Britain along with the indistinguishable model fits based on Eqs. 13 and 14.
See this image and copyright information in PMC

References

    1. Anderson, R. M. & May, R. M. (1992) Infectious Diseases in Man (Oxford Univ. Press, Oxford).
    1. Department for Environment, Food and Rural Affairs (2005) The Incidence of TB in Cattle–Great Britain. Available at http://statistics.defra.gov.uk/esg/statnot/tbpn.pdf. Accessed September 21, 2005.
    1. Krebs, J. R., Anderson, R. M., Clutton-Brock, T., Morrison, W. I., Young, D. & Donnelly, C. A. (1997) Bovine Tuberculosis in Cattle and Badgers (MAFF, London) No. PB3423.
    1. Krebs, J. R., Anderson, R. M., Clutton-Brock, T., Donnelly, C. A., Frost, S., Morrison, W. I., Woodroffe, R. & Young, D. (1998) Science 279, 817–818. - PubMed
    1. Dunnet, G. M., Jones, D. M. & McInerney, J. P. (1986) Badgers and Bovine Tuberculosis (HMSO, London).