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arXiv · 1903.08027

The Viral State Dynamics of the Discrete-Time NIMFA Epidemic Model

Bastian Prasse·Piet Van Mieghem
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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.

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Bastian Prasse, Piet Van Mieghem. 2019-03-19. The Viral State Dynamics of the Discrete-Time NIMFA Epidemic Model. https://arxiv.org/abs/1903.08027

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