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Exact equations for SIR epidemics on tree graphs

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posted on 2023-06-21, 06:01 authored by K J Sharkey, Istvan Kiss, R R Wilkinson, P L Simon
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Bulletin of Mathematical Biology

ISSN

0092-8240

Publisher

Springer Verlag

Issue

4

Volume

77

Page range

614-645

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-09-01

First Open Access (FOA) Date

2016-09-01

First Compliant Deposit (FCD) Date

2016-09-01

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