Abstract
The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition for large-scale propagation, as encoded in the epidemic threshold. Despite the great interest in the problem for the physics, applied mathematics, computer science and epidemiology communities, a full theoretical understanding is still missing and currently limited to the cases where the time-scale separation holds between spreading and network dynamics or to specific temporal network models. We consider a Markov chain description of the Susceptible-Infectious-Susceptible process on an arbitrary temporal network. By adopting a multilayer perspective, we develop a general analytical derivation of the epidemic threshold in terms of the spectral radius of a matrix that encodes both network structure and disease dynamics. The accuracy of the approach is confirmed on a set of temporal models and empirical networks and against numerical results. In addition, we explore how the threshold changes when varying the overall time of observation of the temporal network, so as to provide insights on the optimal time window for data collection of empirical temporal networked systems. Our framework is both of fundamental and practical interest, as it offers novel understanding of the interplay between temporal networks and spreading dynamics.
Highlights
A wide range of physical, social, and biological phenomena can be expressed in terms of spreading processes on interconnected substrates
Much research has focused on spreading processes occurring on time-varying networks [16,17,21,23,24,25,26,27,28,29,30,31], modeled either as a discrete-time sequence of networks [16,28] or as continuous-time dynamics of links [17,26]; so far, only a few studies have provided an analytical calculation of the epidemic threshold in specific cases [24,27,28,29,30,31,32]
For both directed and undirected networks [38,39], the study of the asymptotic state yields the derivation of the epidemic threshold ðλ=μÞ 1⁄4 1=ρðA†Þ, where ρðA†Þ is the spectral radius of the transposed adjacency matrix A† [8,9]. This is known to be a lower bound estimate of the real epidemic threshold, approaching the real value with surprisingly high accuracy given the simplicity of the expression and its derivation [37,40]. We extend this paradigm to a temporal network by letting the adjacency matrix in Eq (1) depend on time: pðitÞ
Summary
A wide range of physical, social, and biological phenomena can be expressed in terms of spreading processes on interconnected substrates. Much research has focused on spreading processes occurring on time-varying networks [16,17,21,23,24,25,26,27,28,29,30,31], modeled either as a discrete-time sequence of networks [16,28] or as continuous-time dynamics of links [17,26]; so far, only a few studies have provided an analytical calculation of the epidemic threshold in specific cases [24,27,28,29,30,31,32]. The role of the observation time window is analyzed in depth in order to provide indications on how this factor alters the estimated epidemic threshold
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call