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Correlations between stochastic endemic infection in multiple interacting subpopulations.

Sophie R Meakin1, Matt J Keeling2

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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.

Keywords:
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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.