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Laws of large numbers for epidemic models with countably many types


Barbour, A D; Luczak, M J (2008). Laws of large numbers for epidemic models with countably many types. Annals of Applied Probability, 18(6):2208-2238.

Abstract

In modeling 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 ℓ1-norm.

In modeling 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 ℓ1-norm.

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7 citations in Web of Science®
7 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:04 Mar 2009 08:34
Last Modified:05 Apr 2016 13:07
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
Free access at:Related URL. An embargo period may apply.
Publisher DOI:10.1214/08-AAP521
Related URLs:http://projecteuclid.org/euclid.aoap/1227708917
http://arxiv.org/abs/0802.1478v3
Permanent URL: http://doi.org/10.5167/uzh-16904

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