Accuracy criterion for mean field approximations of Markov processes on hypergraphs

TL;DR

This paper establishes error bounds for the NIMFA approximation in hypergraph-structured Markov processes, validating its accuracy in modeling complex interactions in epidemiology, physics, and opinion dynamics.

Contribution

It extends mean-field approximation error analysis to hypergraphs with multi-individual interactions, justifying common modeling assumptions.

Findings

NIMFA is accurate when vertices have many neighbors.

Error bounds are provided for hypergraph-structured processes.

The results support the use of NIMFA in complex network models.

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.