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The SEIR Dynamic Evolutionary Model with Markov Chains in Hyper Networks

Author

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  • Jia Wang

    (School of Science, Dalian Maritime University, Dalian 116026, China)

  • Zhiping Wang

    (School of Science, Dalian Maritime University, Dalian 116026, China)

  • Ping Yu

    (School of Science, Dalian Maritime University, Dalian 116026, China)

  • Peiwen Wang

    (School of Maritime Economics and Management, Dalian Maritime University, Dalian 116026, China)

Abstract

In real life, individuals play an important role in the social networking system. When an epidemic breaks out the individual’s recovery rate depends heavily on the social network in which he or she lives. For this reason, in this paper a nonlinear coupling dynamic model on the hyper network was built. The upper layer is the dynamic social network under the hypernetwork vision, and the lower layer is the physical contact layer. Thus, the dynamic evolutionary coupling mechanism between the social network and epidemic transmission was established. At the same time, this paper deduced the evolution process of the dynamic system according to the Markov chain method. The probability equation of the dynamic evolution process was determined, and the threshold of epidemic spread on the non-uniform network was obtained. In addition, numerical simulations verified the correctness of the theory and the validity of the model. The results show that an individual’s recovery state will be affected by the individual’s social ability and the degree of information forgetting. Finally, suitable countermeasures are suggested to suppress the pandemic from spreading in response to the coupling model’s affecting factors.

Suggested Citation

  • Jia Wang & Zhiping Wang & Ping Yu & Peiwen Wang, 2022. "The SEIR Dynamic Evolutionary Model with Markov Chains in Hyper Networks," Sustainability, MDPI, vol. 14(20), pages 1-16, October.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:20:p:13036-:d:939719
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    References listed on IDEAS

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    1. Fan, Chong-jun & Jin, Yang & Huo, Liang-an & Liu, Chen & Yang, Yun-peng & Wang, Ya-qiong, 2016. "Effect of individual behavior on the interplay between awareness and disease spreading in multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 523-530.
    2. Shi, Tianyu & Long, Ting & Pan, Yaohui & Zhang, Wensi & Dong, Chao & Yin, Qiuju, 2019. "Effects of asymptomatic infection on the dynamical interplay between behavior and disease transmission in multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    3. Ran, Maojie & Chen, Jiancu, 2021. "An information dissemination model based on positive and negative interference in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    4. Wang, Zhishuang & Guo, Quantong & Sun, Shiwen & Xia, Chengyi, 2019. "The impact of awareness diffusion on SIR-like epidemics in multiplex networks," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 134-147.
    5. Chao Zuo & Anjing Wang & Fenping Zhu & Zeyang Meng & Xueke Zhao & xiaoke xu, 2021. "A New Coupled Awareness-Epidemic Spreading Model with Neighbor Behavior on Multiplex Networks," Complexity, Hindawi, vol. 2021, pages 1-14, March.
    6. Saif, M. Ali, 2019. "Epidemic threshold for the SIRS model on the networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    7. Koeneman, Scott H. & Cavanaugh, Joseph E., 2022. "An improved asymptotic test for the Jaccard similarity index for binary data," Statistics & Probability Letters, Elsevier, vol. 184(C).
    8. Ping Huang & Xiao-Long Chen & Ming Tang & Shi-Min Cai & Ye Wu, 2021. "Coupled Dynamic Model of Resource Diffusion and Epidemic Spreading in Time-Varying Multiplex Networks," Complexity, Hindawi, vol. 2021, pages 1-11, March.
    9. Wang, Huan & Ma, Chuang & Chen, Han-Shuang & Zhang, Hai-Feng, 2021. "Effects of asymptomatic infection and self-initiated awareness on the coupled disease-awareness dynamics in multiplex networks," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    10. Huang, He & Chen, Yahong & Ma, Yefeng, 2021. "Modeling the competitive diffusions of rumor and knowledge and the impacts on epidemic spreading," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    11. Jia, Mengqi & Li, Xin & Ding, Li, 2021. "Epidemic spreading with awareness on multi-layer activity-driven networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 579(C).
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    4. Yu, Jiating & Leng, Jiacheng & Sun, Duanchen & Wu, Ling-Yun, 2023. "Network Refinement: Denoising complex networks for better community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).

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