Explicit solutions of the Bass and SI models on hypernetworks

TL;DR

This paper derives exact explicit solutions for the Bass and SI models on various infinite hypernetwork structures, advancing understanding of dynamics with multi-body interactions.

Contribution

It provides the first explicit, exact solutions for these models on hypernetworks with 3-body interactions, including different infinite hypernetwork types.

Findings

Exact expressions for adoption/infection levels on hypernetworks

Solutions applicable to infinite complete hypernetworks and hyperlines

No approximations used in deriving the solutions

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 Erd\H{o}s-R\'enyi hypernetworks, and on infinite hyperlines. These expressions are exact, as they are derived without making any approximation.