Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks

•We study the epidemic spreading in complex heterogeneous networks based on an SIRS model.•The dynamics of the network-based SIRS model is completely determined by a threshold value R0.•If R01 then there exists uniquely an endemic equilibrium which is globally asymptotically stable.•We also consider...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2014-04, Vol.19 (4), p.1042-1054
Main Authors: Li, Chun-Hsien, Tsai, Chiung-Chiou, Yang, Suh-Yuh
Format: Article
Language:English
Subjects:
Asymptotic properties
Communities
Community structure
Complex network
Computer simulation
Epidemic model
Epidemics
Global stability
Lyapunov function
Mathematical models
Networks
Series (mathematics)
Spreading
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Summary:•We study the epidemic spreading in complex heterogeneous networks based on an SIRS model.•The dynamics of the network-based SIRS model is completely determined by a threshold value R0.•If R01 then there exists uniquely an endemic equilibrium which is globally asymptotically stable.•We also consider the effect of network community structure on the epidemic dynamics. In this paper, we study the spreading of infections in complex heterogeneous networks based on an SIRS epidemic model with birth and death rates. We find that the dynamics of the network-based SIRS model is completely determined by a threshold value. If the value is less than or equal to one, then the disease-free equilibrium is globally attractive and the disease dies out. Otherwise, the disease-free equilibrium becomes unstable and in the meantime there exists uniquely an endemic equilibrium which is globally asymptotically stable. A series of numerical experiments are given to illustrate the theoretical results. We also consider the SIRS model in the clustered scale-free networks to examine the effect of network community structure on the epidemic dynamics.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2013.08.033