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

Journal Article (2020)
Author(s)

Bastian Prasse (TU Delft - Network Architectures and Services)

P. Van Mieghem (TU Delft - Network Architectures and Services)

Research Group
Network Architectures and Services
Copyright
© 2020 B. Prasse, P.F.A. Van Mieghem
DOI related publication
https://doi.org/10.1007/s00285-020-01542-6
More Info
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Publication Year
2020
Language
English
Copyright
© 2020 B. Prasse, P.F.A. Van Mieghem
Research Group
Network Architectures and Services
Issue number
6-7
Volume number
81
Pages (from-to)
1299-1355
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Abstract

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.

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