Cluster Synchronization of Individuals During an Epidemic: A Contraction-Based Analysis

Abstract

This article investigates cluster synchronization (CS) of individuals during an epidemic using a coupled nonlinear network that integrates diffusion-coupled nonlinear systems with an susceptible-infected-recovered (SIR) virus model. To better reflect real-life scenarios, individuals are grouped into clusters, and the model incorporates recovery rates that vary according to collective behavior patterns. The study focuses on analyzing the relationship between CS behavior and the progression of virus transmission within the network. By ensuring that the directed graph satisfies the cluster input equivalence condition and that the system’s Jacobian matrix remains bounded, contraction analysis is employed to establish conditions for achieving CS, which are influenced by the virus’s state. Furthermore, the impact of CS on epidemic dynamics is explored. Numerical simulations validate the theoretical findings.