Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems -- especially social ones -- are characterized by clustered substructures representing either collections of all-to-all pair-wise interactions (cliques) and/or group interactions, involving many of their members at once. In this work we focus on interaction structures represented as simplicial complexes, in which a group interaction is identified with a face. We present a microscopic discrete-time  model of complex contagion for which a susceptible-infected-susceptible dynamics is considered . Introducing a particular edge clique cover and a heuristic to find it, the model accounts for the high-order state correlations among the members of the substructures (cliques/simplices). The mathematical tractability of the model allows for the analytical computation of the epidemic threshold, thus extending to structured populations some primary features of the critical properties of mean-field models. Overall, the model is found in remarkable agreement with numerical simulations .
Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections of all-to-all pair-wise interactions (cliques) and/or group interactions, involving many of their members at once. In this work , focusing on interaction structures represented as simplicial complexes, we present a discrete-time microscopic model of complex contagion for a susceptible-infected-susceptible dynamics . Introducing a particular edge clique cover and a heuristic to find it, the model accounts for the higher-order dynamical correlations among the members of the substructures (cliques/simplices). The analytical computation of the critical point reveals that higher-order correlations are responsible for its dependence on the higher-order couplings. While such dependence eludes any mean-field model, the possibility of a bi-stable region is extended to structured populations .
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in which a group interaction is identified with a face. We present a microscopic
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high-order state
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mathematical tractability of the model allows for the
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epidemic threshold, thus extending to structured populations some primary features of the critical properties of
critical point reveals that higher-order correlations are responsible for its dependence on the higher-order couplings. While such dependence eludes any
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models. Overall, the model is found in remarkable agreement with numerical simulations
model, the possibility of a bi-stable region is extended to structured populations