PhysRevLett.115.078701.pdf (346.99 kB)
Generalization of pairwise models to non-Markovian epidemics on networks
journal contribution
posted on 2023-06-08, 22:34 authored by Istvan Kiss, Gergely Röst, Vizi ZsoltIn this Letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations, which shows excellent agreement with results based on stochastic simulations. Furthermore, we analytically compute a new R0-like threshold quantity and an analytical relation between this and the final epidemic size. Additionally, we show that the pairwise model and the analytic results can be generalized to an arbitrary distribution of the infectious times, using integro-differential equations, and this leads to a general expression for the final epidemic size. By showing the rigorous link between non-Markovian dynamics and pairwise delay differential equations, we provide the framework for a more systematic understanding of non-Markovian dynamics.
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- Published
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- Published version
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Physical Review Letters (PRL)ISSN
0031-9007Publisher
American Physical SocietyExternal DOI
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7Volume
115Page range
078701Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2015-09-21First Open Access (FOA) Date
2016-12-07First Compliant Deposit (FCD) Date
2015-09-21Usage metrics
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