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Correlative Microscopy for 3D Structural Analysis of Dynamic Interactions
Published on: June 24, 2013
Correlations between stochastic endemic infection in multiple interacting subpopulations
Sophie R Meakin1, Matt J Keeling2
1EPSRC & MRC Centre for Doctoral Training in Mathematics for Real-World Systems, University of Warwick, UK.
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.
Insights
Understanding disease spread in heterogeneous populations is key. This study reveals how network structure influences infection correlations, simplifying disease modeling and potentially enabling inference from case data.
Area of Science:
- Epidemiology
- Mathematical Biology
- Network Science
Background:
- Infectious disease dynamics are significantly influenced by population heterogeneity.
- Metapopulation models capture spatial heterogeneity by analyzing interactions within and between subpopulations.
- Directly measuring these interactions (couplings) is challenging; correlations are often the observable metric.
Purpose of the Study:
- To investigate the relationship between interaction strength (coupling) and observed correlations in metapopulation models.
- To analyze this relationship across different complex network structures (complete, k-regular tree, star networks).
- To develop a simplified method for understanding endemic disease behavior in heterogeneous systems.
Main Methods:
- Utilized moment-closure methods to analyze systems of multiple identical interacting populations.
- Focused on highly symmetric complex network topologies.
- Derived analytical expressions for correlations based on coupling and network/epidemiological parameters.
Main Results:
- Established a straightforward mathematical form for the correlation between infection prevalence.
- Demonstrated that this correlation is solely dependent on coupling, network characteristics, and epidemiological parameters.
- Showcased the impact of metapopulation network structure on disease dynamics.
Conclusions:
- Metapopulation network structure critically affects endemic disease dynamics.
- Detailed epidemiological data may suffice to infer interaction strengths between populations.
- This research offers a pathway to more accurate mathematical models of infectious disease behavior.
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