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arXiv · 1212.2172

Exact equations for SIR epidemics on tree graphs

Kieran J. Sharkey·Istvan Z. Kiss·Robert R. Wilkinson·Peter L. Simon
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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.

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Kieran J. Sharkey, Istvan Z. Kiss, Robert R. Wilkinson, Peter L. Simon. 2012-12-10. Exact equations for SIR epidemics on tree graphs. https://doi.org/10.1007/s11538-013-9923-5

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