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Laws of large numbers for epidemic models with countably many types

By A. D. Barbour and Malwina J. Luczak

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

Topics: QA Mathematics
Publisher: Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science
Year: 2006
OAI identifier: oai:eprints.lse.ac.uk:13799
Provided by: LSE Research Online
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