title: Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.
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.
authors.affiliation: Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary.|Numerical Analysis and Large Networks Research Group, Hungarian Academy of Sciences, Budapest, Hungary.
authors.forename: András
authors.initials: A
authors.lastname: Szabó-Solticzky
authors.affiliation: Centre for Computational Neuroscience and Robotics, University of Sussex, Falmer, Brighton, BN1 9QH, UK.
authors.forename: Luc
authors.initials: L
authors.lastname: Berthouze
authors.affiliation: Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, BN1 9QH, UK. i.z.kiss@sussex.ac.uk.
authors.forename: Istvan Z
authors.initials: IZ
authors.lastname: Kiss
authors.affiliation: Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary.|Numerical Analysis and Large Networks Research Group, Hungarian Academy of Sciences, Budapest, Hungary.
authors.forename: Péter L
authors.initials: PL
authors.lastname: Simon
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission; D003198:Computer Simulation; D058872:Epidemics / Q000706:statistics & numerical data; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D013269:Stochastic Processes
keywords: Dynamic network; Oscillation; Pairwise model; SIS epidemic