2009/12/30 by A. D. Barbour, Barbour, A. D., Malwina Luczak +2
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #60B12 #60J27 #92D30 #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60B12 #msc:60J27 #msc:92D30
paper · pdf · doi:10.48550/arxiv.1001.0044
revised version in response to referee comments, 34 pages
openalex publication_date 2009/12/30 · arxiv created 2011/03/31 · arxiv updated 2011/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since the population size has no natural upper limit, this leads to systems in which there are countably infinitely many possible types of individual. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove a law of large numbers for rather general systems of this kind, together with a rather sharp bound on the rate of convergence in an appropriately chosen weighted ℓ1 norm.