Exact Equations for SIR Epidemics on Tree Graphs

K. J. Sharkey, I. Z. Kiss, R. R. Wilkinson, L. P. Simon

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph. Moreover, this "deterministic" representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalBulletin of Mathematical Biology
DOIs
Publication statusAccepted/In press - 2013

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Time series
time series analysis
time series
Graph in graph theory
infection
Moment Closure
Infection
Siméon Denis Poisson
Contact
Cycle
Invariant
Evaluate
removal

Keywords

  • Dimensional reduction
  • Kolmogorov equation

ASJC Scopus subject areas

  • Pharmacology
  • Neuroscience(all)
  • Mathematics(all)
  • Immunology
  • Environmental Science(all)
  • Computational Theory and Mathematics
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)

Cite this

Exact Equations for SIR Epidemics on Tree Graphs. / Sharkey, K. J.; Kiss, I. Z.; Wilkinson, R. R.; Simon, L. P.

In: Bulletin of Mathematical Biology, 2013, p. 1-32.

Research output: Contribution to journalArticle

Sharkey, K. J. ; Kiss, I. Z. ; Wilkinson, R. R. ; Simon, L. P. / Exact Equations for SIR Epidemics on Tree Graphs. In: Bulletin of Mathematical Biology. 2013 ; pp. 1-32.
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