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

Kaiyuan Sun,Andrea Baronchelli,Nicola Perra

doi:10.1140/epjb/e2015-60568-4

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 show that while memory inhibits the spreading process in SIR models, where the epidemic threshold is moved to larger values, it plays the opposite effect in the case of the SIS, where the threshold is lowered. The heterogeneity in tie strengths, and the frequent repetition of connections that 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 evaluating the threshold of both processes in a real temporal network. Our findings confirm the important role played by non-Markovian network dynamics on dynamical processes

Highlights

Any system can be represented as a network whose basic units are described as nodes and its interactions as links between them [1,2,3,4]
In this paper we investigate numerically the epidemic dynamics occurring on with memory (WM) networks
We studied the dynamical properties of SIR and SIS models in activity driven networks with and without correlations between contacts

Summary

Introduction

Any system can be represented as a network whose basic units are described as nodes and its interactions as links between them [1,2,3,4]. While such an approximation allows analytical treatments [32,33,34,35,36,38], it does not capture many real properties of time-varying networks such as the memory of individuals. This limitation has been overcome with the introduction of a non-Markovian generalization of the modeling framework that introduces correlations between contacts allowing to reproduce with accuracy the evolution of individual’s contacts [29]. Consistently to what observed in synthetic networks, the real non-Markovian dynamics hampers the disease spreading reducing significantly the final fraction of recovered nodes

Activity driven models

SIR and SIS models in activity driven networks

The SIS process on ML and WM networks

SIS and SIR models in real time varying networks

Conclusions