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

Journal article (2020)

Authors

B. Prasse Network Architectures and Services - EEMCS
P.F.A. Van Mieghem Network Architectures and Services - EEMCS
Research Group
Network Architectures and Services (EEMCS) (TU Delft)
Copyright: © 2020 B. Prasse, P.F.A. Van Mieghem
DOI
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https://doi.org/10.1007/s00285-020-01542-6
SIS process Epidemic models NIMFA differential equations Viral state dynamics
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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Quantum & Computer Engineering

Research Group

Network Architectures and Services

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.