Time-dependent solution of the NIMFA equations around the epidemic threshold

Bastian Prasse*, Piet Van Mieghem

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
13 Downloads (Pure)


The majority of epidemic models are described by non-linear differential equations which do not have a closed-form solution. Due to the absence of a closed-form solution, the understanding of the precise dynamics of a virus is rather limited. We solve the differential equations of the N-intertwined mean-field approximation of the susceptible-infected-susceptible epidemic process with heterogeneous spreading parameters around the epidemic threshold for an arbitrary contact network, provided that the initial viral state vector is small or parallel to the steady-state vector. Numerical simulations demonstrate that the solution around the epidemic threshold is accurate, also above the epidemic threshold and for general initial viral states that are below the steady-state.

Original languageEnglish
Pages (from-to)1299-1355
Number of pages57
JournalJournal of Mathematical Biology
Issue number6-7
Publication statusPublished - 2020


  • Epidemic models
  • NIMFA differential equations
  • SIS process
  • Viral state dynamics


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