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Epidemic spreading with nonlinear infectivity in weighted scale-free networks

Author

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  • Chu, Xiangwei
  • Zhang, Zhongzhi
  • Guan, Jihong
  • Zhou, Shuigeng

Abstract

In this paper, we investigate the epidemic spreading for the SIR model in weighted scale-free networks with the nonlinear infectivity and weighted transmission rate. Concretely, we introduce the infectivity exponent α and the weight exponent β into the epidemic system, then examine the impact of α and β on the epidemic spreading. We show that one can adjust the values of α and β to rebuild a nonzero finite epidemic threshold. Furthermore, we also find the infectivity exponent α has a stronger effect not only on the epidemic threshold, but also on the epidemic prevalence. In addition, it is also interesting to see that the absence of the epidemic threshold appears not very dejected, since the prevalence grows much more slowly as the transmission rate λ increases.

Suggested Citation

  • Chu, Xiangwei & Zhang, Zhongzhi & Guan, Jihong & Zhou, Shuigeng, 2011. "Epidemic spreading with nonlinear infectivity in weighted scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(3), pages 471-481.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:3:p:471-481
    DOI: 10.1016/j.physa.2010.09.038
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
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    Cited by:

    1. Liu, Xiongding & Li, Tao & Xu, Hao & Liu, Wenjin, 2019. "Spreading dynamics of an online social information model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 497-510.
    2. Fu, Minglei & Yang, Hongbo & Feng, Jun & Guo, Wen & Le, Zichun & Lande, Dmytro & Manko, Dmytro, 2018. "Preferential information dynamics model for online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 993-1005.
    3. Christel Kamp & Mathieu Moslonka-Lefebvre & Samuel Alizon, 2013. "Epidemic Spread on Weighted Networks," PLOS Computational Biology, Public Library of Science, vol. 9(12), pages 1-10, December.
    4. Xiang, Hong & Liu, Ying-Ping & Huo, Hai-Feng, 2017. "Stability of an SAIRS alcoholism model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 276-292.
    5. Wei, Daijun & Deng, Xinyang & Zhang, Xiaoge & Deng, Yong & Mahadevan, Sankaran, 2013. "Identifying influential nodes in weighted networks based on evidence theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2564-2575.
    6. Zhang, Yuhuai & Zhu, Jianjun, 2019. "Dynamic behavior of an I2S2R rumor propagation model on weighted contract networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    7. Meng, Xueyu & Cai, Zhiqiang & Si, Shubin & Duan, Dongli, 2021. "Analysis of epidemic vaccination strategies on heterogeneous networks: Based on SEIRV model and evolutionary game," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    8. Gao, Cai & Wei, Daijun & Hu, Yong & Mahadevan, Sankaran & Deng, Yong, 2013. "A modified evidential methodology of identifying influential nodes in weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5490-5500.
    9. Nian, Fuzhong & Hu, Chasheng & Yao, Shuanglong & Wang, Longjing & Wang, Xingyuan, 2018. "An immunization based on node activity," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 228-233.
    10. Brandi, Giuseppe & Di Clemente, Riccardo & Cimini, Giulio, 2018. "Epidemics of liquidity shortages in interbank markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 255-267.
    11. Huo, Hai-Feng & Cui, Fang-Fang & Xiang, Hong, 2018. "Dynamics of an SAITS alcoholism model on unweighted and weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 249-262.
    12. Wang, Yanhui & Bi, Lifeng & Lin, Shuai & Li, Man & Shi, Hao, 2017. "A complex network-based importance measure for mechatronics systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 180-198.

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