Extinction times for closed epidemics: The effects of host spatial structure

Ecology Letters

Volumn 5, Issue 6, 2002, Pages 747-755

  Park, Andrew W ^a   Gubbins, Simon ^a,b,c   Gilligan, Christopher A ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b CHURCHILL COLLEGE   (United Kingdom)

^c VETERINARY LABORATORIES AGENCY   (United Kingdom)

Author keywords

Epidemiology; Metapopulation; Persistence; Stochastic model

Indexed keywords

EPIDEMIC; EPIDEMIOLOGY; METAPOPULATION; PERSISTENCE;

ILEX COOKII;

EID: 0036847746     PISSN: 1461023X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1461-0248.2002.00378.x     Document Type: Article

References (22)

1. Anderson, R.M. & May, R.M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford.
2. Ball, F.G. & Lyne, O.D. (2002). Optimal vaccination policies for stochastic epidemics among a population of households. Math. Biosci., 177-178, 333-354.
3. Ball, F.G., Mollison, D. & Scalia-Tomba, G. (1997). Epidemics in populations with two levels of mixing. Ann. Appl. Prob., 7, 46-89.
4. Barbour, A.D. (1975). The Mathematical Theory of Infectious Disease and its Applications. Griffin, London.
5. Bartlett, M.S. (1956). Deterministic and stochastic models for recurrent epidemics. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (ed. Neyman, J.). University of California Press, Berkeley, pp. 84-94.
6. Bolker, B.M. & Grenfell, B.T. (1995). Space, persistence and dynamics of measles epidemics. Phil. Trans. R. Soc. Lond. B, 348, 309-320.
7. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol., 28, 365-382.
8. Evans, M., Hastings, N. & Peacock, B. (1993). Statistical Distributions. John Wiley, New York.
9. Ferguson, N.M., Donnelly, C.A. & Anderson, R.M. (2001). Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain. Nature, 414, 542-548.
10. Fieburg, J. & Ellner, S.P. (2001). Stochastic matrix models for conservation and management: A comparative review of methods. Ecol. Lett., 4, 244-266.
11. Gubbins, S. & Gilligan, C.A. (1997). Persistence of host-parasite interactions in a disturbed environment. J. Theor. Biol., 188, 241-258.
12. Kareiva, P. (1990). Population dynamics in spatially complex environments: Theory and data. Phil. Trans. R. Soc. Lond., B330, 175-190.
13. Keeling, M.J., Woolhouse, M.E.J., Shaw, D.J., Matthews, L., Chase-Topping, M., Haydon, D.T. et al. (2001). Dynamics of the 2001 UK foot and mouth epidemic: Stochastic dispersal in a heterogeneous landscape. Science, 294, 813-817.
14. Morris, R.S., Wilesmith, J.W., Stern, M.W., Sanson, R.L. & Stevenson, M.A. (2001). Predictive spatial modelling of alternative control strategies for the foot-and-mouth disease epidemic in Great Britain, 2001. Vet. Record, 149, 137-144.
15. Onstad, D.W. & Kornkven, E.A. (1992). Persistence and endemicity of pathogens in plant populations over time and space. Phytopathology, 82, 561-566.
16. Park, A.W., Gubbins, S. & Gilligan, C.A. (2001). Invasion and persistence of plant parasites in a spatially-structured host population. Oikos, 94, 162-174.
17. Ridler-Rowe, C.J. (1967). On a stochastic model of an epidemic. J. Appl. Prob., 4, 19-33. Ross, G.J.S. (1990). Nonlinear Estimation. Springer-Verlag, London.
18. Shea, K., Thrall, P.H. & Burdon, J.J. (2000). An integrated approach to management in epidemiology, and pest control. Ecol. Lett., 3, 150-108.
19. Swinton, J. (1998). Extinction times and phase transitions for spatially-structured closed epidemics. Bull. Math. Biol., 60, 215-230.
20. Swinton, J., Harwood, J., Grenfell, B.T. & Gilligan, C.A. (1998). Persistence thresholds for phocine distemper virus infection in harbour seal Phoca vitulina metapopulations. J. Anim. Ecol., 67, 54-68.
21. Thrall, P.H. & Burdon, J.J. (1999). The spatial scale of pathogen dispersal: Consequences for disease dynamics and persistence. Evol. Ecol. Res., 1, 681-701.
22. Webb, C.R. & Sauter-Louis, C. (2002). Investigation into the contact structure of the British sheep population. Proceedings of a Meeting Held at Robinson College, University of Cambridge 3rd-5th April 2002 (eds Menzies, F.D. & Reid, S.W.J.). Society for Veterinary Epidemiology and Preventive Medicine, Roslin, UK, pp. 10-20.