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Bounds on the velocity of spread of infection for a spatially connected epidemic process

Published online by Cambridge University Press:  14 July 2016

M. J. Faddy  and
I. H. Slorach
M. J. Faddy*
Affiliation:
University of Birmingham
I. H. Slorach
Affiliation:
University of Queensland
*
∗Postal address: Department of Mathematical Statistics, University of Birmingham, P.O. Box 363, Birmingham B15 2TT, U.K. Research carried out while this author was on leave at the University of Queensland.
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Abstract

The simple (non-spatial) stochastic epidemic is generalised to allow infected individuals to move forward through a system of spatially connected colonies C1, C2, C3, ·· ·each containing susceptible individuals. Upper and lower bounding processes are considered, to establish bounds on the asymptotic velocity of forward spread of the infection through these spatially connected colonies. These bounds are shown to be asymptotically equivalent under certain conditions, and some simulations reveal other features of the process.

Keywords

SPATIAL EPIDEMIC PROCESSSPATIALLY CONNECTED COLONIESBOUNDING PROCESSESVELOCITY OF SPREAD OF INFECTIONRENEWAL PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 839 - 845
Copyright
Copyright © Applied Probability Trust 1980 

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References

Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and its Applications. Griffin, London.Google Scholar
Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
Faddy, M. J. (1979) Partial stochastic/deterministic models in epidemic theory (abstract). Adv. Appl. Prob. 11, 295–296.CrossRefGoogle 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
Renshaw, E. (1977) Velocities of propagation for stepping-stone models of population growth. J. Appl. Prob. 14, 591–597.CrossRefGoogle Scholar
Whittle, P. (1955) The outcome of a stochastic epidemic — a note on Bailey's paper. Biometrika 42, 116–122.Google Scholar