Journal of Mathematical Biology

, Volume 67, Issue 2, pp 411–432 | Cite as

Outbreak analysis of an SIS epidemic model with rewiring

Article

Abstract

This paper is devoted to the analysis of the early dynamics of an SIS epidemic model defined on networks. The model, introduced by Gross et al. (Phys Rev Lett 96:208701, 2006), is based on the pair-approximation formalism and assumes that, at a given rewiring rate, susceptible nodes replace an infected neighbour by a new susceptible neighbour randomly selected among the pool of susceptible nodes in the population. The analysis uses a triple closure that improves the widely assumed in epidemic models defined on regular and homogeneous networks, and applies it to better understand the early epidemic spread on Poisson, exponential, and scale-free networks. Two extinction scenarios, one dominated by transmission and the other one by rewiring, are characterized by considering the limit system of the model equations close to the beginning of the epidemic. Moreover, an analytical condition for the occurrence of a bistability region is obtained.

Keywords

Pair approximation Network epidemic models Rewiring Basic reproduction number 

Mathematics Subject Classification

92D30 (epidemiology) 05C82 (small world graphs, complex networks) 34C60 (qualitative investigation and simulation of models) 90B15 (network models, stochastic) 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Departament d’Informàtica i Matemàtica AplicadaUniversitat de GironaGironaSpain

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