A Low-Dimensional Network Model for an SIS Epidemic: Analysis of the Super Compact Pairwise Model

TL;DR

This paper analyzes a low-dimensional network model for SIS epidemic spread, deriving key epidemiological thresholds and equilibria, and assessing sensitivity to network parameters to inform disease control strategies.

Contribution

It introduces a simplified yet accurate pairwise model for SIS epidemics, providing analytical tools for thresholds and endemic states.

Findings

Epidemic threshold derived for the model

Bifurcation analysis reveals disease persistence conditions

Approximate endemic equilibrium formulated and tested

Abstract

Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the complex dynamics induced by the network structure. We analyze one recently introduced model and derive important epidemiological quantities for the system. We derive the epidemic threshold and analyze the bifurcation that occurs, and we use asymptotic techniques to derive an approximation for the endemic equilibrium when it exists. We consider the sensitivity of this approximation to network parameters, and the implications for disease control measures are found to be in line with the results of existing studies.