Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis

András Szabó-Solticzky, Luc Berthouze, Istvan Z. Kiss, L. P. Simon

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models.

Original languageEnglish
Pages (from-to)1153-1176
Number of pages24
JournalJournal of Mathematical Biology
Volume72
Issue number5
DOIs
Publication statusPublished - Apr 1 2016

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Mean-field Model
Dynamic Networks
Stochastic Simulation
Fourier Analysis
Stochastic models
Mean Field
Network Model
Dynamic Model
Bifurcation Analysis
Master Equation
Deletion
Stochastic Model
Activation
Pairwise
Fourier analysis
Oscillation
Propagation
Dependent
Approximation
Chemical activation

Keywords

  • Dynamic network
  • Oscillation
  • Pairwise model
  • SIS epidemic

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Modelling and Simulation

Cite this

Oscillating epidemics in a dynamic network model : stochastic and mean-field analysis. / Szabó-Solticzky, András; Berthouze, Luc; Kiss, Istvan Z.; Simon, L. P.

In: Journal of Mathematical Biology, Vol. 72, No. 5, 01.04.2016, p. 1153-1176.

Research output: Contribution to journalArticle

Szabó-Solticzky, András ; Berthouze, Luc ; Kiss, Istvan Z. ; Simon, L. P. / Oscillating epidemics in a dynamic network model : stochastic and mean-field analysis. In: Journal of Mathematical Biology. 2016 ; Vol. 72, No. 5. pp. 1153-1176.
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