  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.
