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Epidemic Spread in Networks: Existing Methods and CurrentChallenges

Published online by Cambridge University Press:  24 April 2014

J. C. Miller  and
I. Z. Kiss
J. C. Miller*
Affiliation:
School of Mathematical Sciences, School of Biological Sciences, and Monash Academy for Cross & Interdisciplinary Mathematics, Monash University, VIC 3800, Australia
I. Z. Kiss
Affiliation:
School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK
*
⋆JCM dedicates this work to the memory of Bob Borrelli, who taught him how to useintegrating factors and much more.
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Abstract

We consider the spread of infectious disease through contact networks of ConfigurationModel type. We assume that the disease spreads through contacts and infected individualsrecover into an immune state. We discuss a number of existing mathematical models used toinvestigate this system, and show relations between the underlying assumptions of themodels. In the process we offer simplifications of some of the existing models. Thedistinctions between the underlying assumptions are subtle, and in many if not most casesthis subtlety is irrelevant. Indeed, under appropriate conditions the models areequivalent. We compare the benefits and disadvantages of the different models, and discusstheir application to other populations (e.g., clustered networks).Finally we discuss ongoing challenges for network-based epidemic modeling.

Keywords

epidemicSIR diseasenetworkpairwiseeffective degreeedge-based compartmental modelsconfiguration model networks
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 2: Epidemics models on networks , 2014 , pp. 4 - 42
Copyright
© EDP Sciences, 2014

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