Infections on Temporal Networks--A Matrix-Based Approach

Andreas Koher; Hartmut H K Lentz; Philipp Hövel; Igor M Sokolov

doi:10.1371/journal.pone.0151209

Infections on Temporal Networks--A Matrix-Based Approach

PLoS One. 2016 Apr 1;11(4):e0151209. doi: 10.1371/journal.pone.0151209. eCollection 2016.

Authors

Andreas Koher¹, Hartmut H K Lentz², Philipp Hövel^{1

3}, Igor M Sokolov⁴

Affiliations

¹ Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
² Institute of Epidemiology, Friedrich-Loeffler-Institute, Südufer 10, 17493 Greifswald, Germany.
³ Bernstein Center for Computational Neuroscience Berlin, Humboldt Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany.
⁴ Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.

Abstract

We extend the concept of accessibility in temporal networks to model infections with a finite infectious period such as the susceptible-infected-recovered (SIR) model. This approach is entirely based on elementary matrix operations and unifies the disease and network dynamics within one algebraic framework. We demonstrate the potential of this formalism for three examples of networks with high temporal resolution: networks of social contacts, sexual contacts, and livestock-trade. Our investigations provide a new methodological framework that can be used, for instance, to estimate the epidemic threshold, a quantity that determines disease parameters, for which a large-scale outbreak can be expected.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Animals
Communicable Diseases / epidemiology*
Communicable Diseases / transmission
Community Networks
Computer Simulation
Disease Outbreaks
Humans
Livestock
Models, Biological
Sexual Partners

Grants and funding

AK and PH acknowledge funding by the Deutsche Forschungsgemeinschaft in the framework of the Collaborative Research Center (SFB) 910. PH was partially supported by the Federal Ministry of Education and Research (BMBF), Germany (grant no. 01GQ1001B). IMS acknowledges support by the Deutsche Forschungsgemeinschaft in the framework of the International Research Training Group (IRTG) 1740. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.