The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 18, Number 6 (2008), 2208-2238.
Laws of large numbers for epidemic models with countably many types
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.
Ann. Appl. Probab., Volume 18, Number 6 (2008), 2208-2238.
First available in Project Euclid: 26 November 2008
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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