Journal of Mathematical Biology

, Volume 72, Issue 5, pp 1153–1176 | Cite as

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

  • András Szabó-Solticzky
  • Luc Berthouze
  • Istvan Z. Kiss
  • Péter L. Simon


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.


SIS epidemic Pairwise model Dynamic network Oscillation 

Mathematics Subject Classification

05C82 60J28 92D30 34C23 



Péter L. Simon acknowledges support from the Hungarian Scientific Research Fund (OTKA) (Grant No. 81403).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • András Szabó-Solticzky
    • 1
    • 2
  • Luc Berthouze
    • 3
  • Istvan Z. Kiss
    • 4
  • Péter L. Simon
    • 1
    • 2
  1. 1.Institute of MathematicsEötvös Loránd UniversityBudapestHungary
  2. 2.Numerical Analysis and Large Networks Research GroupHungarian Academy of SciencesBudapestHungary
  3. 3.Centre for Computational Neuroscience and RoboticsUniversity of SussexBrightonUK
  4. 4.Department of Mathematics, School of Mathematical and Physical SciencesUniversity of SussexBrightonUK

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