SIS/R model on Bi-Uniform Hypergraph

TL;DR

This paper develops and analyzes an SIS/R epidemic model on bi-uniform hypergraphs, deriving exact differential equations, making approximations, and validating results through stochastic simulations.

Contribution

It generalizes existing SIS models to include SIR dynamics on hypergraphs, providing exact equations and numerical solutions for bi-uniform hypergraphs.

Findings

Derived exact differential equations for SIS/SIR on hypergraphs

Validated numerical solutions against stochastic simulations

Extended model applicability to bi-uniform hypergraphs

Abstract

This report is based on the work in (1). We first review definitions and notation developped there and provide derivations for the exact mathematical description of an SIS epidemic on a hypergraph. We then generalise the work in (1) to a new class of models that encompass SIS and SIR models. The exact differential equations are derived for the expected values of the population of each state. Focusing on Bi-uniform hypergraphs, we make suitable approximations obtain numerical solutions to those equations. These are compared with stochastic simulations of the model for various systems.