Exact Equations for SIR Epidemics on Tree Graphs

Sharkey, K. J. and Kiss, I. Z. and Wilkinson, R. R. and Simon L., Péter (2015) Exact Equations for SIR Epidemics on Tree Graphs. BULLETIN OF MATHEMATICAL BIOLOGY, 77 (4). pp. 614-45. ISSN 0092-8240

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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. © 2013 Society for Mathematical Biology.

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