Prevalence expansion in NIMFA

The N-Intertwined Mean Field Approximation (NIMFA) is a reasonably accurate approximation of the exact SIS epidemic process on a network. The average fraction of infected nodes in the NIMFA steady state, also called the steady-state prevalence, in terms of the effective infection rate can be expanded into a power series around the NIMFA epidemic threshold. In this paper, we investigate the convergence of the steady-state prevalence Taylor expansion. We determine the radius of convergence in some special types of graphs. We also show that the radius of convergence of the steady-state prevalence expansion depends upon the network topology, in particular, the average degree of the network and the spectral gap of the adjacency matrix play a role.