Explicit solutions of the Bass and SI models on hypernetworks
Abstract
We analyze the Bass model and the Susceptible-Infected (SI) model on hypergraphs with 3-body interactions. We derive the master equations for general hypernetworks, and use them to obtain explicit expressions for the expected adoption/infection level on infinite complete hypernetworks, infinite Erdos-R\'enyi hypernetworks, and on infinite hyperlines. These expressions are exact, as they are derived without making any approximation.
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