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Pairwise approximation for SIR-type network epidemics with non-Markovian recovery
journal contribution
posted on 2023-06-09, 12:08 authored by G Rost, Z Vizi, Istvan KissWe present the generalized mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic partial differential equation (PDE) system, where the population of infective nodes and links are structured by age since infection. We show that the PDE system can be reduced to a system of integro-differential equations, which is analysed analytically and numerically. We investigate the asymptotic behaviour of the generalized model and provide an implicit analytical expression involving the final epidemic size and pairwise reproduction number. As an illustration of the applicability of the general model, we recover known results for the exponentially distributed and fixed recovery time cases. For gamma- and uniformly distributed infectious periods, new pairwise models are derived. Theoretical findings are confirmed by comparing results from the new pairwise model and explicit stochastic network simulation. A major benefit of the generalized pairwise model lies in approximating the time evolution of the epidemic.
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Publication status
- Published
File Version
- Accepted version
Journal
Proceedings of the Royal Society A: Mathematical, Physical and Engineering ScienceISSN
1364-5021Publisher
The Royal SocietyExternal DOI
Issue
2210Volume
474Page range
1-21Article number
a20170695Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-02-14First Open Access (FOA) Date
2018-02-14First Compliant Deposit (FCD) Date
2018-02-14Usage metrics
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