Exact equations for SIR epidemics on tree graphs

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.

33 pages, 7 figures

References in corpus (4)

• A message passing approach for general epidemic models
• Edge-Based Compartmental Modeling for Infectious Disease Spread Part I: An Overview
• Large graph limit for an SIR process in random network with heterogeneous connectivity
• Edge-based compartmental modeling for epidemic spread Part II: Model Selection and Hierarchies

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• Mean-field models of dynamics on networks via moment closure: an automated procedure
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