Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-14T07:41:03.087Z Has data issue: false hasContentIssue false

Waveforms and velocities for models of spatial infection

Published online by Cambridge University Press:  14 July 2016

Eric Renshaw*
Affiliation:
University of Edinburgh
*
Postal address: Department of Statistics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Rd., Edinburgh EH9 3JZ, U.K.

Abstract

A new technique is developed for deriving velocities of propagation and shapes of travelling wave profiles in non-linear situations. Two models are considered for the spread of infection through a linear community. In one the infected individuals move, in the other the phenomenon of infection.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Daniels, H. E. (1975) The deterministic spread of a simple epidemic. In Perspectives in Probability and Statistics, ed. Gani, J., distributed by Academic Press, London for the Applied Probability Trust, Sheffield, 373386.Google Scholar
Faddy, M. J. and Slorach, I. H. (1980) Bounds on the velocity of spread of infection for a spatially connected epidemic process. J. Appl. Prob. 17, 839845.CrossRefGoogle Scholar
Kendall, D. G. (1965) Mathematical models of the spread of infection. In Mathematics and Computer Science in Biology and Medicine, MRC, HMSO, London, 213225.Google Scholar
Mollison, D. (1972) The rate of spatial propagation of simple epidemics. Proc. 6th Berkeley Symp. Math. Statist. Prob. 3, 579614.Google Scholar
Mollison, D. (1977) Spatial contact models for ecological and epidemic spread (with discussion). J. R. Statist. Soc. B39, 283326.Google Scholar
Renshaw, E. (1972) Birth, death and migration processes. Biometrika 59, 4960.CrossRefGoogle Scholar
Renshaw, E. (1974) Stepping-stone models for population growth. J. Appl. Prob. 11, 1631.CrossRefGoogle Scholar
Renshaw, E. (1977) Velocities of propagation for stepping-stone models of population growth. J. Appl. Prob. 14, 591597.CrossRefGoogle Scholar
Renshaw, E. (1979) Waveforms and velocities for non-nearest-neighbour contact distributions. J. Appl. Prob. 16, 111.CrossRefGoogle Scholar