Modelling epidemics on d-cliqued graphs

  • Laura P. Schaposnik University of Illinois at Chicago, Chicago, IL, USA; Freie Universität Berlin, Berlin, Germany;
  • Anlin Zhang Canyon Crest Academy, San Diego, CA, USA
Keywords: Epidemic dynamics, cliques, symmetric graphs

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.

Published
2018-12-14
How to Cite
Schaposnik, Laura, and Anlin Zhang. 2018. “Modelling Epidemics on D-Cliqued Graphs”. Letters in Biomathematics 5 (1), 49-69. https://doi.org/10.1080/23737867.2017.1419080.
Section
Research