Cluster collective behaviors via feedback pinning control induced by epidemic spread in a patchy population with dispersal

Pan Yang; Jianwen Feng; Xinchu Fu; Pan Yang; Jianwen Feng; Xinchu Fu

doi:10.3934/mbe.2020259

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 4718-4746. doi: 10.3934/mbe.2020259

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Research article

Cluster collective behaviors via feedback pinning control induced by epidemic spread in a patchy population with dispersal

1.
Department of Mathematics, Shanghai University, Shanghai 200444, China
2.
College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China

Received: 24 March 2020 Accepted: 30 June 2020 Published: 08 July 2020

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.
- behavior cluster synchronization,
- patch dispersal,
- epidemic spread,
- feedback pinning control,
- complex network
Citation: Pan Yang, Jianwen Feng, Xinchu Fu. Cluster collective behaviors via feedback pinning control induced by epidemic spread in a patchy population with dispersal[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4718-4746. doi: 10.3934/mbe.2020259

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Abstract

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.

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