Correlations between stochastic endemic infection in multiple interacting subpopulations

Sophie R Meakin,Matt J Keeling

doi:10.1016/j.jtbi.2019.109991

Abstract

Heterogeneity plays an important role in the emergence, persistence and control of infectious diseases. Metapopulation models are often used to describe spatial heterogeneity, and the transition from random- to heterogeneous-mixing is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. We use moment-closure methods to investigate how the coupling and resulting correlation are related, considering systems of multiple identical interacting populations on highly symmetric complex networks: the complete network, the k-regular tree network, and the star network. We show that the correlation between the prevalence of infection takes a relatively simple form and can be written in terms of the coupling, network parameters and epidemiological parameters only. These results provide insight into the effect of metapopulation network structure on endemic disease dynamics, and suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour.

Highlights

IntroductionHeterogeneity is an increasingly important feature of epidemiological models, with spatial structure (Grenfell and Bolker, 1998; Xia et al, 2004; Viboud et al, 2006), risk structure (Baguelin et al, 2010; Datta et al, 2018; Rock et al, 2018) and age structure (Schenzle, 1984; Keeling and Grenfell, 1997; Keeling and White, 2010) widely considered
In the complete network metapopulation all subpopulations are epidemiologically and topologically identical: epidemiologically in the sense that all subpopulations are of equal size and have identical epidemiological parameters, and topologically in the sense that all nodes are isomorphic within the network and the coupling is the same between any pair of subpopulations
Our results provide insight into the effect of metapopulation network structure on endemic disease dynamics, but further work is required before it may be implemented in a real world setting

Summary

Introduction

Heterogeneity is an increasingly important feature of epidemiological models, with spatial structure (Grenfell and Bolker, 1998; Xia et al, 2004; Viboud et al, 2006), risk structure (Baguelin et al, 2010; Datta et al, 2018; Rock et al, 2018) and age structure (Schenzle, 1984; Keeling and Grenfell, 1997; Keeling and White, 2010) widely considered. The parameter-free radiation model (Simini et al, 2012) and variants thereof (Yan et al, 2014; Kang et al, 2015) offer alternative models for human mobility that only requires the spatial distribution of the population to estimate coupling. Comparisons between both the gravity and radiation models, and mobile call data records show that these models fail to fully describe human mobility outside of high-income countries, such as in Sub-Saharan Africa (Wesolowski et al, 2015)

Methods

Results

Discussion

Conclusion