## Abstract

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.

Original language | English |
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Article number | 123220 |

Pages (from-to) | 1-13 |

Number of pages | 13 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 540 |

DOIs | |

Publication status | Published - 2020 |

## Keywords

- NIMFA
- Radius of convergence
- SIS prevalence
- Taylor expansion