The Annals of Applied Probability

Laws of large numbers for epidemic models with countably many types

A. D. Barbour and M. J. Luczak

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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 1-norm.

Article information

Source
Ann. Appl. Probab., Volume 18, Number 6 (2008), 2208-2238.

Dates
First available in Project Euclid: 26 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1227708917

Digital Object Identifier
doi:10.1214/08-AAP521

Mathematical Reviews number (MathSciNet)
MR2473655

Zentralblatt MATH identifier
1197.92039

Subjects
Primary: 92D30: Epidemiology 60J27: Continuous-time Markov processes on discrete state spaces 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)

Keywords
Epidemic models infinitely many types quantitative law of large numbers

Citation

Barbour, A. D.; Luczak, M. J. Laws of large numbers for epidemic models with countably many types. Ann. Appl. Probab. 18 (2008), no. 6, 2208--2238. doi:10.1214/08-AAP521. https://projecteuclid.org/euclid.aoap/1227708917


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