Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model

Abstract

Data of physical contacts and face-to-face communications suggest temporally varying networks as the media on which infections take place among humans and animals. Epidemic processes on temporal networks are complicated by complexity of both network structure and temporal dimensions. Theoretical approaches are much needed for identifying key factors that affect dynamics of epidemics. In particular, what factors make some temporal networks stronger media of infection than other temporal networks is under debate. We develop a theory to understand the susceptible-infected-susceptible epidemic model on arbitrary temporal networks, where each contact is used for a finite duration. We show that temporality of networks lessens the epidemic threshold such that infections persist more easily in temporal networks than in their static counterparts. We further show that the Lie commutator bracket of the adjacency matrices at different times is a key determinant of the epidemic threshold in temporal networks. The effect of temporality on the epidemic threshold, which depends on a data set, is approximately predicted by the magnitude of a commutator norm.

arXiv comment8 figures, 1 table

References in corpus (31)

• Epidemic spreading in scale-free networks
• Epidemic processes in complex networks
• Temporal Networks
• Epidemic dynamics on an adaptive network
• High-resolution measurements of face-to-face contact patterns in a primary school
• What's in a crowd? Analysis of face-to-face behavioral networks
• Thresholds for epidemic spreading in networks
• Activity driven modeling of time varying networks
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Modern temporal network theory: A colloquium
• Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys
• Estimating Potential Infection Transmission Routes in Hospital Wards Using Wearable Proximity Sensors
• Information diffusion epidemics in social networks
• Impact of non-Poisson activity patterns on spreading processes
• Contact patterns among high school students
• The dynamical strength of social ties in information spreading
• Fluctuating epidemics on adaptive networks
• Mitigation of infectious disease at school: targeted class closure vs school closure
• Information dynamics shape the networks of Internet-mediated prostitution
• Controlling Contagion Processes in Time-Varying Networks
• Temporal networks: slowing down diffusion by long lasting interactions
• Analytical computation of the epidemic threshold on temporal networks
• Dynamical and bursty interactions in social networks
• Branching Dynamics of Viral Information Spreading
• Epidemic threshold and control in a dynamic network
• Entropy of dynamical social networks
• Epidemic spreading in evolving networks
• Infection propagator approach to compute epidemic thresholds on temporal networks: impact of immunity and of limited temporal resolution
• Interplay of network dynamics and ties heterogeneity on spreading dynamics
• Spread of pathogens in the patient transfer network of US hospitals
• Accelerating coordination in temporal networks by engineering the link order

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• Markovian approach to tackle the interaction of simultaneous diseases
• Containing misinformation spreading in temporal social networks
• Particle velocity controls phase transitions in contagion dynamics
• Fixation probability in evolutionary dynamics on switching temporal networks
• A Parrondo paradox in susceptible-infectious-susceptible dynamics over periodic temporal networks
• Optimal Containment of Epidemics over Temporal Activity-Driven Networks
• Distributed Agreement on Activity Driven Networks
• Compressing the chronology of a temporal network with graph commutators