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Laws of large numbers for epidemic models with countably many types

Barbour, A. D. and Luczak, Malwina J. (2006) Laws of large numbers for epidemic models with countably many types. CDAM research report, LSE-CDAM-2006-14. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

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Abstract

In modelling parasitic diseases, it is natural to distinguish hosts according to the number of parasites that they carry, leading to a countably infinite type space. Proving the analogue of the deterministic equations, used in models with finitely many types as a ‘law of large numbers’ approximation to the underlying stochastic model, has previously either been done case by case, using some special structure, or else not attempted. In this paper, we prove a general theorem of this sort, and complement it with a rate of convergence in the `1-norm.

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk
Additional Information: © 2006 Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2006-14
Date Deposited: 09 Oct 2008 16:01
URL: http://eprints.lse.ac.uk/13799/

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