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.
Highlights
A majority of infectious diseases, ranging from seasonal influenza to Ebola outbreaks and sexually transmitted infections, can be viewed to occur on contact networks of humans and animals, which are composed of individuals and dyadic links between them
We show theoretical and numerical evidence that the epidemic threshold decreases as the network becomes more temporal in the sense that the network changes more slowly relative to the time scale of the epidemic process
We have provided evidence that the epidemic threshold for the SIS model on temporal networks is smaller than that for the corresponding static networks for arbitrary temporal networks
Summary
A majority of infectious diseases, ranging from seasonal influenza to Ebola outbreaks and sexually transmitted infections, can be viewed to occur on contact networks of humans and animals, which are composed of individuals and dyadic links between them. Valdano and colleagues introduced a temporal-network variant of the individual-based approximation to understand the susceptible-infected-susceptible (SIS) model of epidemic spreading [25, 26] ( see [27] for a similar approach to a different disease model). In this approach, the probability that each node is infected is tracked over time using the matrix algebra. They showed how to calculate the epidemic threshold (i.e., strength of infection above which infection can remain prevalent in the population) and the prevalence (i.e., fraction of infected nodes in the stationary state) in terms of the spectral radius of a relevant matrix Their theory is applicable to arbitrary temporal network data. We suppress these refinements for the sake of tractability of the model
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