Exact Equations for SIR Epidemics on Tree Graphs

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

Research output: Contribution to journalArticle

18 Citations (Scopus)


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)614-645
Number of pages32
JournalBulletin of Mathematical Biology
Issue number4
Publication statusPublished - Apr 1 2015



  • Dimensional reduction
  • Kolmogorov equation

ASJC Scopus subject areas

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

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