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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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.

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

First available in Project Euclid: 26 November 2008

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

Epidemic models infinitely many types quantitative law of large numbers


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.

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