University of Sussex
Browse
__smbhome.uscs.susx.ac.uk_bw233_Desktop_SRO_SRO - Istvan Kiss_ComparisonSimonKiss_Revised.pdf (316.83 kB)

On bounding exact models of epidemic spread on networks

Download (316.83 kB)
journal contribution
posted on 2023-06-09, 08:11 authored by Péter L Simon, Istvan Kiss
In 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 B

ISSN

1531-3492

Publisher

American Institute of Mathematical Sciences

Issue

5

Volume

23

Page range

2005-2020

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-10-05

First Open Access (FOA) Date

2019-05-22

First Compliant Deposit (FCD) Date

2017-10-05

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC