Interdependency and hierarchy of exact and approximate epidemic models on networks

Over the years numerous models of SIS (susceptible → infected → susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general motif-based models. We illustrate how the different models can be...

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Bibliographic Details
Published inJournal of mathematical biology Vol. 69; no. 1; pp. 183 - 211
Main Authors Taylor, Timothy J., Kiss, Istvan Z.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2014
Springer Nature B.V
Subjects
Applications of Mathematics
Communicable Diseases - epidemiology
Communicable Diseases - transmission
Computer Simulation
Epidemics
Humans
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Models, Biological
Epidemic
Exact models
00A71
92D30
92D25
Network
00A72
Kolmogorov/master equations
92D40
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Summary:Over the years numerous models of SIS (susceptible → infected → susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general motif-based models. We illustrate how the different models can be derived from one another and, where this is not possible, discuss extensions to established models that enables this derivation. We also derive a general result for the exact differential equations for the expected number of an arbitrary motif directly from the Kolmogorov/master equations and conclude with a comparison of the performance of the different closed systems of equations on networks of varying structure.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-013-0699-x