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Pairwise and Edge-based Models of Epidemic Dynamics onCorrelated Weighted Networks

Published online by Cambridge University Press:  24 April 2014

P. Rattana ,
J.C. Miller  and
I.Z. Kiss
P. Rattana
Affiliation:
School of Mathematical and Physical Sciences, Department of Mathematics University of Sussex, Falmer, Brighton BN1 9QH, UK
J.C. Miller
Affiliation:
School of Mathematical Sciences, School of Biological Sciences, and the Monash Academy for Cross & Interdisciplinary Mathematics, Monash University, , VIC 800, Australia
I.Z. Kiss*
Affiliation:
School of Mathematical and Physical Sciences, Department of Mathematics University of Sussex, Falmer, Brighton BN1 9QH, UK
*
⋆Corresponding author. E-mail: i.z.kiss@sussex.ac.uk
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Abstract

In this paper we explore the potential of the pairwise-type modelling approach to beextended to weighted networks where nodal degree and weights are not independent. As abaseline or null model for weighted networks, we consider undirected, heterogenousnetworks where edge weights are randomly distributed. We show that the pairwise modelsuccessfully captures the extra complexity of the network, but does this at the cost oflimited analytical tractability due the high number of equations. To circumvent thisproblem, we employ the edge-based modelling approach to derive models corresponding to twodifferent cases, namely for degree-dependent and randomly distributed weights. Thesemodels are more amenable to compute important epidemic descriptors, such as early growthrate and final epidemic size, and produce similarly excellent agreement with simulation.Using a branching process approach we compute the basic reproductive ratio for both modelsand discuss the implication of random and correlated weight distributions on this as wellas on the time evolution and final outcome of epidemics. Finally, we illustrate that thetwo seemingly different modelling approaches, pairwise and edge-based, operate on similarassumptions and it is possible to formally link the two.

Keywords

weighted networkpairwise modeledge-based compartmental modellingprobability generating function
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 2: Epidemics models on networks , 2014 , pp. 58 - 81
Copyright
© EDP Sciences, 2014

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