From Markovian to pairwise epidemic models and the performance of moment closure approximations

Michael Taylor, L. P. Simon, Darren M. Green, Thomas House, Istvan Z. Kiss

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise the link between a well known pairwise model and the exact Markovian formulation. This involves the rigorous derivation of the exact ODE model at the level of pairs in terms of the expected number of pairs and triples. The exact system is then closed using two different closures, one well established and one that has been recently proposed. A new interpretation of both closures is presented, which explains several of their previously observed properties. The closed dynamical systems are solved numerically and the results are compared to output from individual-based stochastic simulations. This is done for a range of networks with the same average degree and clustering coefficient but generated using different algorithms. It is shown that the ability of the pairwise system to accurately model an epidemic is fundamentally dependent on the underlying large-scale network structure. We show that the existing pairwise models are a good fit for certain types of network but have to be used with caution as higher-order network structures may compromise their effectiveness.

Original languageEnglish
Pages (from-to)1021-1042
Number of pages22
JournalJournal of Mathematical Biology
Volume64
Issue number6
DOIs
Publication statusPublished - May 2012

Fingerprint

Moment Closure
Epidemic Model
Cluster Analysis
Pairwise
Approximation
Population
Network Structure
Closure
Model
Closed
Clustering Coefficient
Large-scale Structure
Formulation
Stochastic Simulation
closed loop systems
disease transmission
Dynamical systems
Dynamical system
Higher Order
Dependent

Keywords

  • Epidemic
  • Markov chain
  • Moment closure
  • Network

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Modelling and Simulation

Cite this

From Markovian to pairwise epidemic models and the performance of moment closure approximations. / Taylor, Michael; Simon, L. P.; Green, Darren M.; House, Thomas; Kiss, Istvan Z.

In: Journal of Mathematical Biology, Vol. 64, No. 6, 05.2012, p. 1021-1042.

Research output: Contribution to journalArticle

Taylor, Michael ; Simon, L. P. ; Green, Darren M. ; House, Thomas ; Kiss, Istvan Z. / From Markovian to pairwise epidemic models and the performance of moment closure approximations. In: Journal of Mathematical Biology. 2012 ; Vol. 64, No. 6. pp. 1021-1042.
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