Abstract
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 quite general systems of this kind, together with a rather sharp bound on the rate of convergence in an appropriately chosen weighted ℓ 1 norm.
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A.D. Barbour was supported in part by Schweizerischer Nationalfonds Projekt Nr. 20–107935/1.
M.J. Luczak was supported in part by a STICERD grant.
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Barbour, A.D., Luczak, M.J. A law of large numbers approximation for Markov population processes with countably many types. Probab. Theory Relat. Fields 153, 727–757 (2012). https://doi.org/10.1007/s00440-011-0359-2
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DOI: https://doi.org/10.1007/s00440-011-0359-2
Keywords
- Epidemic models
- Metapopulation processes
- Countably many types
- Quantitative law of large numbers
- Markov population processes