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The outcome of a general spatial epidemic on the line

Published online by Cambridge University Press:  14 July 2016

M. J. Faddy
M. J. Faddy*
Affiliation:
University of Birmingham
*
∗ Department of Statistics, University of Birmingham, P.O. Box 363, Birmingham B 15 2TT, U.K.
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Abstract

The general (non-spatial) stochastic epidemic is extended to allow infective individuals to move forward through a system of spatially connected locations · ··, L1, L2, · ·· (on the line) each containing susceptible individuals and the outcome of the epidemic in each of these locations is then considered. In the deterministic case, a (spatial) equilibrium solution and threshold behaviour are discussed. In the stochastic case, a (spatial) quasi-equilibrium behaviour (conditional on sufficient numbers of infectives present) is discussed; numerical results suggest some correspondence between this stochastic quasi-equilibrium and the deterministic equilibrium.

Keywords

SPATIAL EPIDEMIC PROCESSSPATIALLY CONNECTED LOCATIONSOUTCOME OF EPIDEMICDETERMINISTIC EQUILIBRIUM AND THRESHOLDSTOCHASTIC QUASI-EQUILIBRIUMCOMPARISON OF DETERMINISTIC AND STOCHASTIC MODELS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 715 - 727
Copyright
Copyright © Applied Probability Trust 1983 

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References

Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and its Applications. Griffin, London.Google Scholar
Barbour, A. E. (1974) On a functional central limit theorem for Markov population processes. Adv. Appl. Prob. 6, 21–39.Google Scholar
Darroch, J. N. and Seneta, E. (1965) On quasi-stationary distributions in absorbing discrete-time finite Markov chains. J. Appl. Prob. 2, 88–100.CrossRefGoogle Scholar
Faddy, M. J. and Slorach, I. (1980) Bounds on the velocity of spread of infection for a spatially connected epidemic process. J. Appl. Prob. 17, 839–845.Google Scholar
Kendall, D. G. (1957) Discussion contribution to Bartlett, M. S., Measles periodicity and community size. J.R. Statist. Soc. A 120, 64–67.Google Scholar
Mollison, D. (1972) The rate of spatial propagation of simple epidemics. Proc. 6th Berkeley Symp. Math. Statist. Prob. 3, 579–614.Google Scholar
Mollison, D. (1977) Spatial contact models for ecological and epidemic spread (with discussion). J. R. Statist. Soc. B 39, 283–326.Google Scholar
Seneta, E. (1981) Non-negative Matrices and Markov Chains, 2nd edn. Springer-Verlag, New York.CrossRefGoogle Scholar