Feedback pinning control of collective behaviors aroused by epidemic spread on complex networks
Pan Yang, Zhongpu Xu, Jianwen Feng, Xinchu Fu

TL;DR
This paper develops a feedback control strategy to synchronize collective behaviors in complex networks affected by epidemic spread, providing new insights into controlling disease transmission and behavioral responses.
Contribution
It introduces a novel pinning feedback control approach for epidemic-induced behavioral synchronization, combining epidemic models with complex network control theory.
Findings
Derived epidemic threshold using convex functions and Gerschgorin theorem.
Designed two feedback control strategies based on infection status.
Numerical simulations confirm the effectiveness of the proposed control methods.
Abstract
This paper investigates epidemic control behavioral synchronization for a class of complex networks resulting from spread of epidemic diseases via pinning feedback control strategy. Based on the quenched mean field theory, epidemic control synchronization models with inhibition of contact behavior is constructed, combining with the epidemic transmission system and the complex dynamical network carrying extra controllers. By the properties of convex functions and Gerschgorin theorem, the epidemic threshold of the model is obtained, and the global stability of disease-free equilibrium is analyzed. For individual's infected situation, when epidemic spreads, two types of feedback control strategies depended on the diseases' information are designed: the one only adds controllers to infected individuals, the other adds controllers both to infected and susceptible ones. And by using Lyapunov…
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