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A deterministic epidemic model taking account of repeated contacts between the same individuals

Published online by Cambridge University Press:  14 July 2016

O. Diekmann ,
M. C. M. de Jong  and
J. A. J. Metz
O. Diekmann*
Affiliation:
CWI, EEW
M. C. M. de Jong*
Affiliation:
ID-DLO
J. A. J. Metz*
Affiliation:
EEW, International Institute for Applied Systems Analysis
*
∗Postal address: Mathematical Institue, Utrecht University, P.O. Box 80.010, 3508TA Utrecht, The Netherlands. E-mail address: diekmann@math.ruu.nl
∗∗Postal address: ID-DLO, PO Box 65, 8200 AB Lelystad.
∗∗∗Postal address: EEW, section Theoretical Biology, University of Leiden, PO Box 9516, 2300 RA Leiden. The Netherlands.
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Abstract

We introduce a certain population contact structure and derive, in three different ways, the final size equation for a quite general superimposed epidemic process. The contact structure is characterized by the following two properties: (i) each individual contacts exactly k other individuals; (ii) these k acquaintances are a random sample of the (infinite) population.

Keywords

Contact structurebasic reproduction ratiofinal size

MSC classification

Primary: 92D30: Epidemiology
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 448 - 462
Copyright
Copyright © Applied Probability Trust 1998 

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