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Matrix expression and vaccination control for epidemic dynamics over dynamic networks
P.Guo,Y.Wang
0
(School of Control Science and Engineering, Shandong University)
摘要:
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.
关键词:  Epidemic dynamics, dynamic network, vaccination control, semi-tensor product of matrices
DOI:
Received:October 11, 2015Revised:October 14, 2015
基金项目:
Matrix expression and vaccination control for epidemic dynamics over dynamic networks
P. Guo,Y. Wang
(School of Control Science and Engineering, Shandong University)
Abstract:
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.
Key words:  Epidemic dynamics, dynamic network, vaccination control, semi-tensor product of matrices