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An SIS model with infective medium on complex networks

Author

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  • Shi, Hongjing
  • Duan, Zhisheng
  • Chen, Guanrong

Abstract

In this paper, a new susceptible-infected-susceptible model with infective medium is proposed, which describes epidemics (e.g. malaria) transmitted by infective media (e.g. mosquitoes) on various complex networks. The dynamic behaviours of the model on a homogeneous network and a heterogenous scale-free network are considered, respectively, where the absence of the threshold on the scale-free network is demonstrated. Then, analytical and simulated results are given to show that the proportional immunization strategy to the new model is very effective on scale-free networks. Furthermore, it is shown that the immune density of nodes depends not only on the infectivity between individual persons, but also on the infectivity between persons and mosquitoes. This reveals that the absence of a critical immunization threshold not only is due to the unbounded connectivity fluctuation of the underlying scale-free network, but also is determined by the path of the epidemic spreading.

Suggested Citation

  • Shi, Hongjing & Duan, Zhisheng & Chen, Guanrong, 2008. "An SIS model with infective medium on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2133-2144.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:8:p:2133-2144
    DOI: 10.1016/j.physa.2007.11.048
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    Citations

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    Cited by:

    1. Li, Jingjing & Zhang, Yumei & Man, Jiayu & Zhou, Yun & Wu, Xiaojun, 2017. "SISL and SIRL: Two knowledge dissemination models with leader nodes on cooperative learning networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 740-749.
    2. Zhang, Ruixia & Li, Deyu & Jin, Zhen, 2015. "Dynamic analysis of a delayed model for vector-borne diseases on bipartite networks," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 342-352.
    3. Singh, Anurag & Arquam, Md, 2022. "Epidemiological modeling for COVID-19 spread in India with the effect of testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    4. Wang, Dan & Cheng, Shun-Jun, 2016. "A two-stage broadcast message propagation model in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1286-1293.
    5. Zhang, Chunming & Huang, Haitao, 2016. "Optimal control strategy for a novel computer virus propagation model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 251-265.
    6. Xie, Yingkang & Wang, Zhen, 2021. "Transmission dynamics, global stability and control strategies of a modified SIS epidemic model on complex networks with an infective medium," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 23-34.
    7. Juang, Jonq & Liang, Yu-Hao, 2015. "Analysis of a general SIS model with infective vectors on the complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 382-395.
    8. Gong, Yong-Wang & Song, Yu-Rong & Jiang, Guo-Ping, 2013. "Time-varying human mobility patterns with metapopulation epidemic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4242-4251.
    9. Leyi Zheng & Longkun Tang, 2019. "A Node-Based SIRS Epidemic Model with Infective Media on Complex Networks," Complexity, Hindawi, vol. 2019, pages 1-14, February.
    10. Yang, Meng & Chen, Guanrong & Fu, Xinchu, 2011. "A modified SIS model with an infective medium on complex networks and its global stability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2408-2413.
    11. Sanders, Johnathan & Noble, Benjamin & Van Gorder, Robert A. & Riggs, Cortney, 2012. "Mobility matrix evolution for an SIS epidemic patch model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6256-6267.

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