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On bounding exact models of epidemic spread on networks
journal contribution
posted on 2023-06-09, 08:11 authored by Péter L Simon, Istvan KissIn this paper we use comparison theorems from classical ODE theory in order to rigorously show that closures or approximations at individual or node level lead to mean-field models that bound the exact stochastic process from above. This will be done in the context of modelling epidemic spread on networks and the proof of the result relies on the observation that the epidemic process is negatively correlated (in the sense that the probability of an edge being in the susceptible-infected state is smaller than the product of the probabilities of the nodes being in the susceptible and infected states, respectively). The results in the paper hold for Markovian epidemics and arbitrary weighted and directed networks. Furthermore, we cast the results in a more general framework where alternative closures, other than that assuming the independence of nodes connected by an edge, are possible and provide a succinct summary of the stability analysis of the resulting more general mean-field models. While deterministic initial conditions are key to obtain the negative correlation result we show that this condition can be relaxed as long as extra conditions on the edge weights are imposed.
History
Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems - Series BISSN
1531-3492Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
5Volume
23Page range
2005-2020Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-10-05First Open Access (FOA) Date
2019-05-22First Compliant Deposit (FCD) Date
2017-10-05Usage metrics
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