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SIR epidemics on a scale-free spatial nested modular network

Part of: Systems theory and control: General Special processes Equilibrium statistical mechanics

Published online by Cambridge University Press:  24 March 2016

Alberto Gandolfi  and
Lorenzo Cecconi
Alberto Gandolfi*
Affiliation:
Università di Firenze and New York University Abu Dhabi
Lorenzo Cecconi*
Affiliation:
Università di Firenze
*
* Postal address: Dipartimento di Statistica, Informatica, Applicazioni G. Parenti, Università di Firenze, Viale Morgagni 59, 50134 Firenze, Italy. Email address: l.cecconi@disia.unifi.it
** Postal address: Dipartimento di Matematica e Informatica U. Dini, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy. Email address: gandolfi@math.unifi.it
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Abstract

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We propose a class of random scale-free spatial networks with nested community structures called SHEM and analyze Reed–Frost epidemics with community related independent transmissions. We show that in a specific example of the SHEM the epidemic threshold may be trivial or not as a function of the relation among community sizes, distribution of the number of communities, and transmission rates.

Keywords

EpidemicsSIRReed–Frostpercolationlong rangedirectedscale freemodularnestedcommunitieshierarchicalthresholdspatialSHEM

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 92D30: Epidemiology 93A13: Hierarchical systems 82B43: Percolation

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 1 , March 2016 , pp. 137 - 162
Copyright
Copyright © Applied Probability Trust 2016 

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