Accuracy criterion for mean field approximations of Markov processes on hypergraphs

Abstract

We provide error bounds for the N-intertwined mean-field approximation (NIMFA) for local density-dependent Markov population processes with a well-distributed underlying network structure showing NIMFA being accurate when a typical vertex has many neighbors. The result justifies some of the most common approximations used in epidemiology, statistical physics and opinion dynamics literature under certain conditions. We allow interactions between more than 2 individuals, and an underlying hypergraph structure accordingly.

References in corpus (12)

• Epidemic spreading in scale-free networks
• Simplicial models of social contagion
• Activity driven modeling of time varying networks
• Fundamentals of spreading processes in single and multilayer complex networks
• Annealed and Mean-Field formulations of Disease Dynamics on Static and Adaptive Networks
• Dynamics of Majority Rule on Hypergraphs
• Spectral properties and the accuracy of mean-field approaches for epidemics on correlated networks
• Universal mean-field framework for SIS epidemics on networks, based on graph partitioning and the isoperimetric inequality
• Epidemic Outbreaks in Networks with Equitable or Almost-Equitable Partitions
• Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models
• Usefulness of the Age-Structured SIR Dynamics in Modelling COVID-19
• Consensus from group interactions: An adaptive voter model on hypergraphs