Clustering for epidemics on networks: a geometric approach

Journal article

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.

Authors: Prasse, B; Devriendt, K; Van Mieghem, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: AIP Publishing
• Journal: Chaos
• Volume: 31
• Issue: 6
• Article number: 063115
• Place of publication: United States
• Publication date: 2021-06-14
• Acceptance date: 2021-05-06
• DOI: 10.1063/5.0048779
• EISSN: 1089-7682
• ISSN: 1054-1500
• Pmid: 34241312
• Language: English
• Keywords: epidemics; cluster analysis; models; biological; theoretical; disease susceptibility; communicable diseases