Modelling epidemics on d-cliqued graphs. Issue 1 (14th December 2018)

• Record Type: Journal Article
• Authors: Schaposnik, Laura P.; Zhang, Anlin
• Is Part Of: Letters in biomathematics. Volume 5:Issue 1(2018)
• Page Start: 49
• Page End: 69
• Publication Date: 2018-12-14
• Subjects: Epidemic dynamics -- cliques -- symmetric graphs; Biomathematics -- Periodicals; Computational Biology; Biostatistics; Models, Biological; Biomathematics; Periodicals; Periodicals; 570.151
• DOI: 10.1080/23737867.2017.1419080
• Languages: English
• ISSNs: 2373-7867

Abstract

Abstract: Since social interactions have been shown to lead to symmetric clusters, we propose here that symmetries play a key role in epidemic modelling. Mathematical models on d -ary tree graphs were recently shown to be particularly effective for modelling epidemics in simple networks. To account for symmetric relations, we generalize this to a new type of networks modelled on d -cliqued tree graphs, which are obtained by adding edges to regular d -trees to form d -cliques. This setting gives a more realistic model for epidemic outbreaks originating within a family or classroom and which could reach a population by transmission via children in schools. Specifically, we quantify how an infection starting in a clique (e.g. family) can reach other cliques through the body of the graph (e.g. public places). Moreover, we propose and study the notion of a safe zone, a subset that has a negligible probability of infection.