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Dynamics of an SAITS alcoholism model on unweighted and weighted networks

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  • Huo, Hai-Feng
  • Cui, Fang-Fang
  • Xiang, Hong

Abstract

A novel SAITS alcoholism model on networks is introduced, in which alcoholics are divided into light problem alcoholics and heavy problem alcoholics. Susceptible individuals can enter into the compartment of heavy problem alcoholics directly by contacting with light problem alcoholics or heavy problem alcoholics and the heavy problem alcoholics who receive treatment can relapse into the compartment of heavy problem alcoholics are also considered. First, the dynamics of our model on unweighted networks, including the basic reproduction number, existence and stability of equilibria are studied. Second, the models with fixed weighted and adaptive weighted networks are introduced and investigated. At last, some simulations are presented to illustrate and extend our results. Our results show that it is very important to treat alcoholics to quit the drinking.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:496:y:2018:i:c:p:249-262
    DOI: 10.1016/j.physa.2018.01.003
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    References listed on IDEAS

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    1. Wang, Jia-zeng & Liu, Zeng-rong & Xu, Jianhua, 2007. "Epidemic spreading on uncorrelated heterogenous networks with non-uniform transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 715-721.
    2. 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.
    3. 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.
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    Cited by:

    1. Zhang, Xiao-Bing & Chang, Suqin & Shi, Qihong & Huo, Hai-Feng, 2018. "Qualitative study of a stochastic SIS epidemic model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 805-817.
    2. 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.
    3. Wang, Weiming & Cai, Yongli & Ding, Zuqin & Gui, Zhanji, 2018. "A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 921-936.
    4. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.

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