Exact Equations for SIR Epidemics on Tree Graphs

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 t...

Full description

Saved in:
Bibliographic Details
Published inBulletin of mathematical biology Vol. 77; no. 4; pp. 614 - 645
Main Authors Sharkey, K. J., Kiss, I. Z., Wilkinson, R. R., Simon, P. L.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2015
Springer Nature B.V
Subjects
Cell Biology
Communicable Diseases - epidemiology
Computer Simulation
Epidemics - statistics & numerical data
Humans
Life Sciences
Markov Chains
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Statistical
Original
Original Article
Stochastic Processes
Systems Biology
Kolmogorov equation
Dimensional reduction
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-013-9923-5