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The relationship with discrete-time ADN models is straightforward. In a time step (Equation presented), the continuous-time model establishes as many edges as in a realization of the discrete-time model. The activity rate of a node in continuous time corresponds to the product of its activity potential and the number of contacts it can establish in the time step. The probability that an infected node recovers in a discrete-time step is (Equation presented). The per-contact infection probability does not change between continuous and discrete time.
-
The relationship with discrete-time ADN models is straightforward. In a time step (Equation presented), the continuous-time model establishes as many edges as in a realization of the discrete-time model. The activity rate of a node in continuous time corresponds to the product of its activity potential and the number of contacts it can establish in the time step. The probability that an infected node recovers in a discrete-time step is (Equation presented). The per-contact infection probability does not change between continuous and discrete time.
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The original formulation of ADNs posits a continuous power-law distribution with (Equation presented).
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See Supplemental Material at for details about the derivation of the main equations, employed mathematical tools, parameter identification for the case studies, and finite-time horizon predictions for the Twitter case study.
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