Cluster Synchronization of Individuals During an Epidemic: A Contraction-Based Analysis
研究疫情中个体按集群同步的行为，用耦合网络和SIR模型分析同步与病毒传播的关系，通过收缩分析给出同步条件并验证影响。
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.