Abstract
The majority of research on epidemics relies on models which are formulated in continuous-time. However, processing real-world epidemic data and simulating epidemics is done digitally and the continuous-time epidemic models are usually approximated by discrete-time models. In general, there is no guarantee that properties of continuous-time epidemic models, such as the stability of equilibria, also hold for the respective discrete-time approximation. 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 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.
Original language | English |
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Article number | 8864012 |
Pages (from-to) | 1667-1674 |
Number of pages | 8 |
Journal | IEEE Transactions on Network Science and Engineering |
Volume | 7 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Epidemic processes
- nonlinear systems