IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v441y2023ics009630032200769x.html
   My bibliography  Save this article

Thermostated Susceptible-Infected-Susceptible epidemic model

Author

Listed:
  • Alrebdi, H.I.
  • Steklain, Andre
  • Amorim, Edgard P.M.
  • Zotos, Euaggelos

Abstract

The evolution of epidemics based on the Susceptible-Infected-Susceptible (SIS) model relies on the density of infected individuals ρ. Recent results show that the mean density 〈ρ〉 and its variance σ2 can be regarded as canonical variables and obey Hamilton’s equations. Using the Hamiltonian formulation, we study the SIS system coupled to a Nosé thermal bath. We reinterpret classical parameters like temperature in an epidemiological context. In contrast to classical epidemiological models, the thermal bath modifies the dynamical behavior of the system by introducing fluctuations, such as those seen in some infectious waves. We study the stability and show that 〈ρ〉 tends to be half of the value predicted by the original SIS model.

Suggested Citation

  • Alrebdi, H.I. & Steklain, Andre & Amorim, Edgard P.M. & Zotos, Euaggelos, 2023. "Thermostated Susceptible-Infected-Susceptible epidemic model," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    • Handle: RePEc:eee:apmaco:v:441:y:2023:i:c:s009630032200769x
    DOI: 10.1016/j.amc.2022.127701
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032200769X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127701?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhan, Xiu-Xiu & Liu, Chuang & Zhou, Ge & Zhang, Zi-Ke & Sun, Gui-Quan & Zhu, Jonathan J.H. & Jin, Zhen, 2018. "Coupling dynamics of epidemic spreading and information diffusion on complex networks," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 437-448.
    2. Gao, Shujing & Teng, Zhidong & Xie, Dehui, 2009. "Analysis of a delayed SIR epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1004-1011.
    3. Sun, Qingyi & Wang, Zhishuang & Zhao, Dawei & Xia, Chengyi & Perc, Matjaž, 2022. "Diffusion of resources and their impact on epidemic spreading in multilayer networks with simplicial complexes," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Artalejo, J.R. & Lopez-Herrero, M.J., 2011. "The SIS and SIR stochastic epidemic models: A maximum entropy approach," Theoretical Population Biology, Elsevier, vol. 80(4), pages 256-264.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yin, Fulian & Jiang, Xinyi & Qian, Xiqing & Xia, Xinyu & Pan, Yanyan & Wu, Jianhong, 2022. "Modeling and quantifying the influence of rumor and counter-rumor on information propagation dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Chen, Jie & Hu, Mao-Bin & Li, Ming, 2020. "Traffic-driven epidemic spreading dynamics with heterogeneous infection rates," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Chen, Zheng & Wu, Yong-Ping & Feng, Guo-Lin & Qian, Zhong-Hua & Sun, Gui-Quan, 2021. "Effects of global warming on pattern dynamics of vegetation: Wuwei in China as a case," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    4. Dong, Yafang & Huo, Liang'an & Zhao, Laijun, 2022. "An improved two-layer model for rumor propagation considering time delay and event-triggered impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Velarde, Carlos & Robledo, Alberto, 2021. "Statistical mechanical model for growth and spread of contagions under gauged population confinement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    6. Krishnagopal, Sanjukta & Bianconi, Ginestra, 2023. "Topology and dynamics of higher-order multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. You, Xuemei & Zhang, Man & Ma, Yinghong & Tan, Jipeng & Liu, Zhiyuan, 2023. "Impact of higher-order interactions and individual emotional heterogeneity on information-disease coupled dynamics in multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    8. Li, Wenyao & Cai, Meng & Zhong, Xiaoni & Liu, Yanbing & Lin, Tao & Wang, Wei, 2023. "Coevolution of epidemic and infodemic on higher-order networks," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    9. Qu, Hongbo & Song, Yu-Rong & Li, Ruqi & Li, Min, 2023. "GNR: A universal and efficient node ranking model for various tasks based on graph neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P2).
    10. Sudarshan Kumar & Tiziana Di Matteo & Anindya S. Chakrabarti, 2020. "Disentangling shock diffusion on complex networks: Identification through graph planarity," Papers 2001.01518, arXiv.org.
    11. Wei Zhang & Juan Zhang & Yong-Ping Wu & Li Li, 2019. "Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold," Complexity, Hindawi, vol. 2019, pages 1-13, May.
    12. Ganegoda, Naleen & Götz, Thomas & Putra Wijaya, Karunia, 2021. "An age-dependent model for dengue transmission: Analysis and comparison to field data," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    13. Hu, Xin & Wang, Zhishuang & Sun, Qingyi & Chen, Jiaxing & Zhao, Dawei & Xia, Chengyi, 2024. "Coupled propagation between one communicable disease and related two types of information on multiplex networks with simplicial complexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 645(C).
    14. M., Pitchaimani & M., Brasanna Devi, 2020. "Random effects in HIV infection model at Eclipse stage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    15. Chen, Xiaolong & Gong, Kai & Wang, Ruijie & Cai, Shimin & Wang, Wei, 2020. "Effects of heterogeneous self-protection awareness on resource-epidemic coevolution dynamics," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    16. Feng, Meiling & Li, Xuezhu & Zhao, Dawei & Xia, Chengyi, 2023. "Evolutionary dynamics with the second-order reputation in the networked N-player trust game," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    17. Chen, Xiao-Long & Wang, Rui-Jie & Yang, Chun & Cai, Shi-Min, 2019. "Hybrid resource allocation and its impact on the dynamics of disease spreading," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 156-165.
    18. Li, Kun & Chen, Zhiyu & Cong, Rui & Zhang, Jianlei & Wei, Zhenlin, 2024. "Simulated dynamics of virus spreading on social networks with various topologies," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    19. Imane Abouelkheir & Fadwa El Kihal & Mostafa Rachik & Ilias Elmouki, 2019. "Optimal Impulse Vaccination Approach for an SIR Control Model with Short-Term Immunity," Mathematics, MDPI, vol. 7(5), pages 1-21, May.
    20. Meliksah Turker & Haluk O. Bingol, 2023. "Multi-layer network approach in modeling epidemics in an urban town," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-13, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:441:y:2023:i:c:s009630032200769x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.