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Stability of an SAIRS alcoholism model on scale-free networks

Author

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  • Xiang, Hong
  • Liu, Ying-Ping
  • Huo, Hai-Feng

Abstract

A new SAIRS alcoholism model with birth and death on complex heterogeneous networks is proposed. The total population of our model is partitioned into four compartments: the susceptible individual, the light problem alcoholic, the heavy problem alcoholic and the recovered individual. The spread of alcoholism threshold R0 is calculated by the next generation matrix method. When R0<1, the alcohol free equilibrium is globally asymptotically stable, then the alcoholics will disappear. When R0>1, the alcoholism equilibrium is global attractivity, then the number of alcoholics will remain stable and alcoholism will become endemic. Furthermore, the modified SAIRS alcoholism model on weighted contact network is introduced. Dynamical behavior of the modified model is also studied. Numerical simulations are also presented to verify and extend theoretical results. Our results show that it is very important to treat alcoholics to control the spread of the alcoholism.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:473:y:2017:i:c:p:276-292
    DOI: 10.1016/j.physa.2017.01.012
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    References listed on IDEAS

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    1. 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.
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    Cited by:

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    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. Huo, Liang’an & Cheng, Yingying & Liu, Chen & Ding, Fan, 2018. "Dynamic analysis of rumor spreading model for considering active network nodes and nonlinear spreading rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 24-35.
    4. 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.
    5. Huo, Hai-Feng & Xue, Hui-Ning & Xiang, Hong, 2018. "Dynamics of an alcoholism model on complex networks with community structure and voluntary drinking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 880-890.

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