Matrix expression and vaccination control for epidemic dynamics over dynamic networks

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• 作者：Peilian Guo ; Yuzhen Wang
• 关键词：Epidemic dynamics ; dynamic network ; vaccination control ; semi ; tensor product of matrices
• 刊名：Control Theory and Technology
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：14
• 期：1
• 页码：39-48
• 全文大小：2,081 KB
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• 作者单位：Peilian Guo (1)
  Yuzhen Wang (1)
  
  1. School of Control Science and Engineering, Shandong University, Jinan Shandong, 250061, China
  
• 刊物类别：Control; Systems Theory, Control; Optimization; Computational Intelligence; Complexity; Control, Rob
• 刊物主题：Control; Systems Theory, Control; Optimization; Computational Intelligence; Complexity; Control, Robotics, Mechatronics;
• 出版者：South China University of Technology and Academy of Mathematics and Systems Science, CAS
• ISSN：2198-0942

文摘

This paper investigates epidemic dynamics over dynamic networks via the approach of semi-tensor product of matrices. First, a formal susceptible-infected-susceptible epidemic dynamic model over dynamic networks (SISED-DN) is given. Second, based on a class of determinate co-evolutionary rule, the matrix expressions are established for the dynamics of individual states and network topologies, respectively. Then, all possible final spreading equilibria are obtained for any given initial epidemic state and network topology by the matrix expression. Third, a sufficient and necessary condition of the existence of state feedback vaccination control is presented to make every individual susceptible. The study of illustrative examples shows the effectiveness of our new results.