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A Node-Based SIRS Epidemic Model with Infective Media on Complex Networks

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  • Leyi Zheng
  • Longkun Tang

Abstract

We focus on the node-based epidemic modeling for networks, introduce the propagation medium, and propose a node-based Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model with infective media. Theoretical investigations show that the endemic equilibrium is globally asymptotically stable. Numerical examples of three typical network structures also verify the theoretical results. Furthermore, comparison between network node degree and its infected percents implies that there is a strong positive correlation between both; namely, the node with bigger degree is infected with more percents. Finally, we discuss the impact of the epidemic spreading rate of media as well as the effective recovered rate on the network average infected state. Theoretical and numerical results show that (1) network average infected percents go up (down) with the increase of the infected rate of media (the effective recovered rate); (2) the infected rate of media has almost no influence on network average infected percents for the fully connected network and NW small-world network; (3) network average infected percents decrease exponentially with the increase of the effective recovered rate, implying that the percents can be controlled at low level by an appropriate large effective recovered rate.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:2849196
    DOI: 10.1155/2019/2849196
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Wei, Xiaodan & Liu, Lijun & Zhou, Wenshu, 2017. "Global stability and attractivity of a network-based SIS epidemic model with nonmonotone incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 789-798.
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    Cited by:

    1. Wang, Xinhe & Wang, Zhen, 2022. "Bifurcation and propagation dynamics of a discrete pair SIS epidemic model on networks with correlation coefficient," Applied Mathematics and Computation, Elsevier, vol. 435(C).

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