Eur. Phys. J. B (2015) 88: 326
https://doi.org/10.1140/epjb/e2015-60568-4

Regular Article

Contrasting effects of strong ties on SIR and SIS processes in temporal networks^*

¹ Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston MA 02115, USA
² Department of Mathematics, City University London, London EC1V 0HB, UK
³ Centre for Business Network Analysis, University of Greenwich, Park Row, London SE10 9LS, UK

^a e-mail: nicolaperra@gmail.com

Received: 14 July 2015
Received in final form: 2 October 2015
Published online: 9 December 2015

Abstract

Most real networks are characterized by connectivity patterns that evolve in time following complex, non-Markovian, dynamics. Here we investigate the impact of this ubiquitous feature by studying the Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Susceptible (SIS) epidemic models on activity driven networks with and without memory (i.e., Markovian and non-Markovian). We find that memory inhibits the spreading process in SIR models by shifting the epidemic threshold to larger values and reducing the final fraction of recovered nodes. On the contrary, in SIS processes memory reduces the epidemic threshold and, for a wide range of disease parameters, increases the fraction of nodes affected by the disease in the endemic state. The heterogeneity in tie strengths, and the frequent repetition of strong ties it entails, allows in fact less virulent SIS-like diseases to survive in tightly connected local clusters that serve as reservoir for the virus. We validate this picture by studying both processes on two real temporal networks.