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Some comparison results for multitype epidemic models

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Damian Clancy
Damian Clancy*
Affiliation:
University of Newcastle upon Tyne
*
∗ Postal address: Department of Mathematics and Statistics, The University, Newcastle upon Tyne NE1 7RU, UK.
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Abstract

We consider a model for the spread of an epidemic through a population divided into m groups, in which infectives move from group to group and infect only within their current group. For both deterministic and stochastic versions of this model, the effect on the total size of the epidemic of varying the speed with which infectives move between groups is considered. We also compare the distribution of the total size of this model with that of a suitably matched model in which infectives cannot move between groups, but are able to infect outside their own group.

Keywords

DYNAMIC POPULATION EPIDEMICSCONTACT DISTRIBUTION EPIDEMICSSIZE OFEPIDEMICSTOCHASTIC ORDERINGMAJORIZATION

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 39B72: Systems of functional equations and inequalities
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 9 - 21
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Work carried out while the author was in receipt of an SERC research studentship at the University of Nottingham.

References

Ball, F. G. (1983) The threshold behaviour of epidemic models. J. Appl. Prob. 20, 227–241.Google Scholar
Ball, F. G. (1991) Dynamic population epidemic models. Math. Biosci. 107, 299–324.Google Scholar
Ball, F. G. and Clancy, D. (1993) The final outcome of a generalised stochastic multitype epidemic model. Adv. Appl. Prob. 25, 721–736.Google Scholar
Faddy, M. J. (1986) A note on the behaviour of deterministic spatial epidemics. Math. Biosci. 80, 19–22.Google Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.Google Scholar
Mollison, D. (1977) Spatial contact models for ecological and epidemic spread. J. R. Statist. Soc. B 39, 283–326.Google Scholar
Pedler, P. J. (1971) Occupation times for two state Markov chains. J. Appl. Prob. 8, 381–390.Google Scholar
Spiegel, M. R. (1968) Mathematical Handbook. McGraw-Hill, New York.Google Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–491.CrossRefGoogle ScholarPubMed