When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic disease. In a sequence of papers, we prove a law of large numbers and a central limit theorem for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted \(\ell_1\)-norm.
This is joint work with Andrew Barbour.