title: SIS Epidemic Propagation on Hypergraphs.
abstract: Mathematical modelling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact master equations of the propagation process are derived for an arbitrary hypergraph given by its incidence matrix. Based on these, moment closure approximation and mean-field models are introduced and compared to individual-based stochastic simulations. The simulation algorithm, developed for networks, is extended to hypergraphs. The effects of hypergraph structure and the model parameters are investigated via individual-based simulation results.
authors.affiliation: Institute of Mathematics, Eötvös Loránd University Budapest, Budapest, Hungary.|Numerical Analysis and Large Networks Research Group, Hungarian Academy of Sciences, Budapest, Hungary.
authors.forename: Ágnes
authors.initials: Á
authors.lastname: Bodó
authors.affiliation: Numerical Analysis and Large Networks Research Group, Hungarian Academy of Sciences, Budapest, Hungary.|Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, Hungary.
authors.forename: Gyula Y
authors.initials: GY
authors.lastname: Katona
authors.affiliation: Institute of Mathematics, Eötvös Loránd University Budapest, Budapest, Hungary. simonp@cs.elte.hu.|Numerical Analysis and Large Networks Research Group, Hungarian Academy of Sciences, Budapest, Hungary. simonp@cs.elte.hu.
authors.forename: Péter L
authors.initials: PL
authors.lastname: Simon
mesh_terms: D000465:Algorithms; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D003198:Computer Simulation; D004198:Disease Susceptibility / Q000453:epidemiology; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D015233:Models, Statistical; D013269:Stochastic Processes
keywords: Exact master equation; Hypergraph; Mean-field model; SIS epidemic