Abstract
Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly describe social contagion, where individuals acquire new norms or ideas after simultaneous exposure to multiple sources of infections. Simplicial contagion has been proposed as an alternative framework where simplices are used to encode group interactions of any order. The presence of these higher-order interactions leads to explosive epidemic transitions and bistability. In particular, critical mass effects can emerge even for infectivity values below the standard pairwise epidemic threshold, where the size of the initial seed of infectious nodes determines whether the system would eventually fall in the endemic or the healthy state. Here we extend simplicial contagion to time-varying networks, where pairwise and higher-order simplices can be created or destroyed over time. By following a microscopic Markov chain approach, we find that the same seed of infectious nodes might or might not lead to an endemic stationary state, depending on the temporal properties of the underlying network structure, and show that persistent temporal interactions anticipate the onset of the endemic state in finite-size systems. We characterize this behavior on higher-order networks with a prescribed temporal correlation between consecutive interactions and on heterogeneous simplicial complexes, showing that temporality again limits the effect of higher-order spreading, but in a less pronounced way than for homogeneous structures. Our work suggests the importance of incorporating temporality, a realistic feature of many real-world systems, into the investigation of dynamical processes beyond pairwise interactions.
Highlights
Contagion processes, from the spread of diseases to opinions and rumors, are ubiquitous in nature [1,2,3]
We begin by comparing contagion processes in static simplicial complexes and in higher-order networks that change over time
We consider random simplicial complexes (RSCs) with N = 500 nodes generated following the algorithm introduced in Ref. [23]
Summary
From the spread of diseases to opinions and rumors, are ubiquitous in nature [1,2,3]. This means that the same number of initially infected agents might or might not lead to an endemic stationary state, depending on the temporal properties of the underlying network structure To this aim, we propose a simple model to tune the degree of temporal correlations in synthetic structures that evolve over time, and investigate how this variable affects the long-term outcome of the spreading dynamics. MMCAs have been extended to temporal networks, allowing for an analytical computation of the epidemic threshold [45], and more recently to simplicial complexes, though in this context the non-linear term associated to contagion in 2-simplices only allows a numerical solution [25] According to this approach, the probability of a generic node i to be infected at time t + 1 is pi(t + 1) = (1 − qi(t)qi, (t))(1 − pi(t)) + (1 − μ)pi(t), (1). In contrast with Ref. [25], here Γi(t) and ∆i(t) are functions of time, and allow us to generalize the MMCA approach to evolving simplicial complexes
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