LAWS OF LARGE NUMBERS FOR EPIDEMIC MODELS WITH COUNTABLY MANY TYPES

• 成果类型: Article
• 署名作者: Barbour, A. D.; Luczak, M. J.
• 署名单位: University of Zurich; University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP521
• 发表日期: 2008
• 页码: 2208-2238
• 关键词: parasitic infection; limit theorem; approximation

摘要

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 l(1)-norm.