Clustering for epidemics on networks: a geometric approach
Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analyzing and controlling an epidemic outbreak. For some contact networks, it is possible to group individuals into clusters. A high-level description of the epidem...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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AIP Publishing
2021
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| _version_ | 1826314980182458368 |
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| author | Prasse, B Devriendt, K Van Mieghem, P |
| author_facet | Prasse, B Devriendt, K Van Mieghem, P |
| author_sort | Prasse, B |
| collection | OXFORD |
| description | Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analyzing and controlling an epidemic outbreak. For some contact networks, it is possible to group individuals into clusters. A high-level description of the epidemic between a few clusters is considerably simpler than on an individual level. However, to cluster individuals, most studies rely on equitable partitions, a rather restrictive structural property of the contact network. In this work, we focus on Susceptible-Infected-Susceptible (SIS) epidemics, and our contribution is threefold. First, we propose a geometric approach to specify all networks for which an epidemic outbreak simplifies to the interaction of only a few clusters. Second, for the complete graph and any initial viral state vectors, we derive the closed-form solution of the nonlinear differential equations of the N-intertwined mean-field approximation of the SIS process. Third, by relaxing the notion of equitable partitions, we derive low-complexity approximations and bounds for epidemics on arbitrary contact networks. Our results are an important step toward understanding and controlling epidemics on large networks. |
| first_indexed | 2024-12-09T03:17:48Z |
| format | Journal article |
| id | oxford-uuid:fc73da75-14b1-4685-b71d-3380ea7fd6e8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:17:48Z |
| publishDate | 2021 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:fc73da75-14b1-4685-b71d-3380ea7fd6e82024-10-18T15:31:19ZClustering for epidemics on networks: a geometric approachJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fc73da75-14b1-4685-b71d-3380ea7fd6e8EnglishSymplectic ElementsAIP Publishing2021Prasse, BDevriendt, KVan Mieghem, PInfectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analyzing and controlling an epidemic outbreak. For some contact networks, it is possible to group individuals into clusters. A high-level description of the epidemic between a few clusters is considerably simpler than on an individual level. However, to cluster individuals, most studies rely on equitable partitions, a rather restrictive structural property of the contact network. In this work, we focus on Susceptible-Infected-Susceptible (SIS) epidemics, and our contribution is threefold. First, we propose a geometric approach to specify all networks for which an epidemic outbreak simplifies to the interaction of only a few clusters. Second, for the complete graph and any initial viral state vectors, we derive the closed-form solution of the nonlinear differential equations of the N-intertwined mean-field approximation of the SIS process. Third, by relaxing the notion of equitable partitions, we derive low-complexity approximations and bounds for epidemics on arbitrary contact networks. Our results are an important step toward understanding and controlling epidemics on large networks. |
| spellingShingle | Prasse, B Devriendt, K Van Mieghem, P Clustering for epidemics on networks: a geometric approach |
| title | Clustering for epidemics on networks: a geometric approach |
| title_full | Clustering for epidemics on networks: a geometric approach |
| title_fullStr | Clustering for epidemics on networks: a geometric approach |
| title_full_unstemmed | Clustering for epidemics on networks: a geometric approach |
| title_short | Clustering for epidemics on networks: a geometric approach |
| title_sort | clustering for epidemics on networks a geometric approach |
| work_keys_str_mv | AT prasseb clusteringforepidemicsonnetworksageometricapproach AT devriendtk clusteringforepidemicsonnetworksageometricapproach AT vanmieghemp clusteringforepidemicsonnetworksageometricapproach |