Central limit approximations for Markov population processes with countably many types

TL;DR

This paper establishes central limit theorems for complex Markov population models with infinitely many types, providing bounds on convergence rates, which are applicable to metapopulation dynamics and disease transmission models.

Contribution

It extends central limit theorem results to systems with countably infinite types and offers convergence rate bounds in weighted $ ext{ell}_1$ norms.

Findings

Proved central limit theorems for infinite-type systems.

Derived bounds on convergence rates.

Applicable to metapopulation and disease transmission models.

Abstract

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 diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted $\ell_1$ norm.