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Epidemic spreading on midscopic multi-layer network with optimal control mechanism

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  • Liu, Yujing
  • Ding, Li
  • An, Xuming
  • Hu, Ping
  • Du, Fuying

Abstract

In this paper, an SIS-based model on heterogeneity, midscopic multi-layer network combining the inter-layer topology with the intra-layer statistical property is proposed. We discuss the global stability of disease-free and endemic equilibrium of the model. Then the dynamic optimization problem of epidemic spreading on multi-layer network is studied considering the heterogeneity of layers. An explicit expression of the optimal solutions is presented in the case where the interaction radius of intra-layer individual is heterogeneous. Numerical simulations are performed to illustrate the obtained theoretical results. It is proved that the optimal control mechanism can effectively minimize specific objective function. Meanwhile, the dynamics of sub-costs is constructed as the cost coefficients varying. Our findings reveal the necessity of studying midscopic networks and demonstrate the underlying interrelationship between individuals behavioral responses and spreading process on multi-layer network.

Suggested Citation

  • Liu, Yujing & Ding, Li & An, Xuming & Hu, Ping & Du, Fuying, 2020. "Epidemic spreading on midscopic multi-layer network with optimal control mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315766
    DOI: 10.1016/j.physa.2019.122775
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    References listed on IDEAS

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    1. Michael McAsey & Libin Mou & Weimin Han, 2012. "Convergence of the forward-backward sweep method in optimal control," Computational Optimization and Applications, Springer, vol. 53(1), pages 207-226, September.
    2. Zhou, Jie & Liu, Zonghua, 2009. "Epidemic spreading in communities with mobile agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1228-1236.
    3. Feng, Yun & Ding, Li & Huang, Yun-Han & Zhang, Li, 2016. "Epidemic spreading on weighted networks with adaptive topology based on infective information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 493-502.
    4. Li, Tao & Liu, Xiongding & Wu, Jie & Wan, Chen & Guan, Zhi-Hong & Wang, Yuanmei, 2016. "An epidemic spreading model on adaptive scale-free networks with feedback mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 649-656.
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    Cited by:

    1. Li, Jingwei & Li, Shouwei, 2023. "Immunization of systemic risk in trade–investment networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).

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