In this paper we investigate cluster collective behaviors aroused by epidemic spread in a patchy population via feedback pinning control strategy. We construct a class of complex network system combined with states feedback behavior synchronization network systems and epidemic spread constant population systems with patch dispersal. In which the dispersal effect among patches are included in the susceptible systems, as well as considering the contact willing function for each patch, determined by the disease’s information and individuals’ behaviors, as the added cofactor before bilinear incidence. On the one hand, we derive conditions about the global asymptotical stability of disease-free equilibrium, and the existence of positive equilibrium. On the other hand, we design states feedback controllers related with the patch disease information to achieve cluster behaviors synchronization. By using the Lyapunov stability analysis method, the global asymptotical stability of the positive equilibrium is discussed, and meanwhile, the criteria for cluster collective behaviors are obtained. Numerical simulations are performed to support our theoretical results.

中文翻译：

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通过由散布在斑驳的人群中的流行病传播引起的反馈钉扎控制来聚集集体行为

在本文中，我们通过反馈固定控制策略，研究了由零散人群中流行病引起的集群集体行为。我们结合状态反馈行为同步网络系统和具有斑块扩散的流行病传播常数种群系统，构建了一类复杂的网络系统。其中，斑块之间的扩散效应包括在易感系统中，并且考虑到由疾病信息和个人行为决定的每个斑块的接触意愿功能，是双线性发病之前增加的辅助因子。一方面，我们推导出无病平衡的全局渐近稳定性和正平衡存在的条件。另一方面，我们设计了与补丁疾病信息相关的状态反馈控制器，以实现集群行为的同步。利用李雅普诺夫稳定性分析方法，讨论了正平衡的全局渐近稳定性，同时，得出了簇群行为的判据。进行数值模拟以支持我们的理论结果。