The Viral State Dynamics of the Discrete-Time NIMFA Epidemic Model
Abstract
The majority of research on epidemics relies on models which are formulated in continuous-time. However, real-world epidemic data is gathered and processed in a digital manner, which is more accurately described by discrete-time epidemic models. We analyse the discrete-time NIMFA epidemic model on directed networks with heterogeneous spreading parameters. In particular, we show that the viral state is increasing and does not overshoot the steady-state, the steady-state is globally exponentially stable, and we provide linear systems that bound the viral state evolution. Thus, the discrete-time NIMFA model succeeds to capture the qualitative behaviour of a viral spread and provides a powerful means to study real-world epidemics.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2019
- DOI:
- 10.48550/arXiv.1903.08027
- arXiv:
- arXiv:1903.08027
- Bibcode:
- 2019arXiv190308027P
- Keywords:
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- Mathematics - Optimization and Control;
- Mathematics - Dynamical Systems;
- Physics - Physics and Society
- E-Print:
- IEEE Transactions on Network Science and Engineering, 7(3), pp.1667-1674 (2020)