IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v421y2022ics0096300321009942.html
   My bibliography  Save this article

Epidemic dynamics on higher-dimensional small world networks

Author

Listed:
  • Wang, Haiying
  • Moore, Jack Murdoch
  • Small, Michael
  • Wang, Jun
  • Yang, Huijie
  • Gu, Changgui

Abstract

Dimension governs dynamical processes on networks. The social and technological networks which we encounter in everyday life span a wide range of dimensions, but studies of spreading on finite-dimensional networks are usually restricted to one or two dimensions. To facilitate investigation of the impact of dimension on spreading processes, we define a flexible higher-dimensional small world network model and characterize the dependence of its structural properties on dimension. Subsequently, we derive mean field, pair approximation, intertwined continuous Markov chain and probabilistic discrete Markov chain models of a COVID-19-inspired susceptible-exposed-infected-removed (SEIR) epidemic process with quarantine and isolation strategies, and for each model identify the basic reproduction number R0, which determines whether an introduced infinitesimal level of infection in an initially susceptible population will shrink or grow. We apply these four continuous state models, together with discrete state Monte Carlo simulations, to analyse how spreading varies with model parameters. Both network properties and the outcome of Monte Carlo simulations vary substantially with dimension or rewiring rate, but predictions of continuous state models change only slightly. A different trend appears for epidemic model parameters: as these vary, the outcomes of Monte Carlo change less than those of continuous state methods. Furthermore, under a wide range of conditions, the four continuous state approximations present similar deviations from the outcome of Monte Carlo simulations. This bias is usually least when using the pair approximation model, varies only slightly with network size, and decreases with dimension or rewiring rate. Finally, we characterize the discrepancies between Monte Carlo and continuous state models by simultaneously considering network efficiency and network size.

Suggested Citation

  • Wang, Haiying & Moore, Jack Murdoch & Small, Michael & Wang, Jun & Yang, Huijie & Gu, Changgui, 2022. "Epidemic dynamics on higher-dimensional small world networks," Applied Mathematics and Computation, Elsevier, vol. 421(C).
  • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300321009942
    DOI: 10.1016/j.amc.2021.126911
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321009942
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2021.126911?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. Liu, Jinzhuo & Meng, Haoran & Wang, Wei & Xie, Zhongwen & Yu, Qian, 2019. "Evolution of cooperation on independent networks: The influence of asymmetric information sharing updating mechanism," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 234-241.
    2. Wang, Haiying & Wang, Jun & Small, Michael & Moore, Jack Murdoch, 2019. "Review mechanism promotes knowledge transmission in complex networks," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 113-125.
    3. Bahbouhi, Jalal Eddine & Moussa, Najem, 2017. "Prisoner’s dilemma game model for e-commerce," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 128-144.
    4. Chad R. Wells & Jeffrey P. Townsend & Abhishek Pandey & Seyed M. Moghadas & Gary Krieger & Burton Singer & Robert H. McDonald & Meagan C. Fitzpatrick & Alison P. Galvani, 2021. "Optimal COVID-19 quarantine and testing strategies," Nature Communications, Nature, vol. 12(1), pages 1-9, December.
    5. Jon M. Kleinberg, 2000. "Navigation in a small world," Nature, Nature, vol. 406(6798), pages 845-845, August.
    6. Xin-Jian Xu & Zhi-Xi Wu & Yong Chen & Ying-Hai Wang, 2004. "Steady States Of Epidemic Spreading In Small-World Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(10), pages 1471-1477.
    7. Mi Feng & Shi-Min Cai & Ming Tang & Ying-Cheng Lai, 2019. "Equivalence and its invalidation between non-Markovian and Markovian spreading dynamics on complex networks," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    8. Wang, Haiying & Wang, Jun & Small, Michael, 2018. "Knowledge transmission model with differing initial transmission and retransmission process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 478-488.
    9. Zhao, Jiuhua & Liu, Qipeng & Wang, Lin & Wang, Xiaofan, 2018. "Prediction of competitive diffusion on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 12-21.
    10. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    11. Zhang, Hai-Feng & Shu, Pan-Pan & Wang, Zhen & Tang, Ming & Small, Michael, 2017. "Preferential imitation can invalidate targeted subsidy policies on seasonal-influenza diseases," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 332-342.
    12. Xingyuan Wang & Zhenzhen Liu & Mogei Wang, 2013. "The Correlation Fractal Dimension Of Complex Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 1-9.
    13. Cai, Shi-Min & Chen, Xuan-Hao & Ye, Xi-Jun & Tang, Ming, 2019. "Precisely identifying the epidemic thresholds in real networks via asynchronous updating," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 377-388.
    14. Wang, Haiying & Moore, Jack Murdoch & Wang, Jun & Small, Michael, 2021. "The distinct roles of initial transmission and retransmission in the persistence of knowledge in complex networks," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    15. Xu, Hedong & Fan, Suohai & Tian, Cunzhi & Xiao, Xinrong, 2019. "Evolutionary investor sharing game on networks," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 138-145.
    16. Zhongzhi Zhang & Yihang Yang & Shuyang Gao, 2011. "Role of fractal dimension in random walks on scale-free networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 84(2), pages 331-338, November.
    17. Li, Cong & Xu, Hedong & Fan, Suohai, 2020. "Synergistic effects of self-optimization and imitation rules on the evolution of cooperation in the investor sharing game," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    18. William J. Bradshaw & Ethan C. Alley & Jonathan H. Huggins & Alun L. Lloyd & Kevin M. Esvelt, 2021. "Bidirectional contact tracing could dramatically improve COVID-19 control," Nature Communications, Nature, vol. 12(1), pages 1-9, December.
    19. Wang, Haiying & Wang, Jun & Ding, Liting & Wei, Wei, 2017. "Knowledge transmission model with consideration of self-learning mechanism in complex networks," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 83-92.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shanshan Chen & Yijun Ran & Hebo Huang & Zhenzhen Wang & Ke-ke Shang, 2022. "Epidemic Dynamics of Two-Pathogen Spreading for Pairwise Models," Mathematics, MDPI, vol. 10(11), pages 1-18, June.

    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. Wang, Haiying & Moore, Jack Murdoch & Wang, Jun & Small, Michael, 2021. "The distinct roles of initial transmission and retransmission in the persistence of knowledge in complex networks," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Zhu, Hongmiao & Jin, Zhen, 2023. "A dynamics model of knowledge dissemination in a WeChat Group from perspective of duplex networks," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    3. Mei, Jun & Wang, Sixin & Xia, Dan & Hu, Junhao, 2022. "Global stability and optimal control analysis of a knowledge transmission model in multilayer networks," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Zhu, Hongmiao & Jin, Zhen & Yan, Xin, 2023. "A dynamics model of coupling transmission for multiple different knowledge in multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    5. Zhu, Hongmiao & Jin, Zhen & Yan, Xin, 2022. "A dynamics model of two kinds of knowledge transmission on duplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    6. Song, Le & Ma, Yinghong, 2022. "Evaluating tacit knowledge diffusion with algebra matrix algorithm based social networks," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    7. Joren Raymenants & Caspar Geenen & Jonathan Thibaut & Klaas Nelissen & Sarah Gorissen & Emmanuel Andre, 2022. "Empirical evidence on the efficiency of backward contact tracing in COVID-19," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    8. Luka Naglić & Lovro Šubelj, 2019. "War pact model of shrinking networks," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-14, October.
    9. Li, Cong & Xu, Hedong & Fan, Suohai, 2021. "Evolutionary compromise game on assortative mixing networks," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    10. Wang, Sixin & Mei, Jun & Xia, Dan & Yang, Zhanying & Hu, Junhao, 2022. "Finite-time optimal feedback control mechanism for knowledge transmission in complex networks via model predictive control," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    11. Zhu, Hongmiao & Wang, Yumie & Yan, Xin & Jin, Zhen, 2022. "Research on knowledge dissemination model in the multiplex network with enterprise social media and offline transmission routes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    12. Guo, Tianjiao & Tu, Lilan & Guo, Yifei & Hu, Jia & Su, Qingqing, 2023. "Control-capacity analysis and optimized construction for controlled interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    13. Liao, Shi-Gen & Yi, Shu-Ping, 2021. "Modeling and analyzing knowledge transmission process considering free-riding behavior of knowledge acquisition: A waterborne disease approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    14. Liao, Shi-Gen & Yi, Shu-Ping, 2021. "Modeling and analysis knowledge transmission process in complex networks by considering internalization mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    15. Tian, Yang & Tian, Hui & Cui, Yajuan & Zhu, Xuzhen & Cui, Qimei, 2023. "Influence of behavioral adoption preference based on heterogeneous population on multiple weighted networks," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    16. Andreas Koulouris & Ioannis Katerelos & Theodore Tsekeris, 2013. "Multi-Equilibria Regulation Agent-Based Model of Opinion Dynamics in Social Networks," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 11(1), pages 51-70.
    17. He, He & Yang, Bo & Hu, Xiaoming, 2016. "Exploring community structure in networks by consensus dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 342-353.
    18. Ellinas, Christos & Allan, Neil & Johansson, Anders, 2016. "Project systemic risk: Application examples of a network model," International Journal of Production Economics, Elsevier, vol. 182(C), pages 50-62.
    19. Yang, Hyeonchae & Jung, Woo-Sung, 2016. "Structural efficiency to manipulate public research institution networks," Technological Forecasting and Social Change, Elsevier, vol. 110(C), pages 21-32.
    20. Andrea Avena-Koenigsberger & Xiaoran Yan & Artemy Kolchinsky & Martijn P van den Heuvel & Patric Hagmann & Olaf Sporns, 2019. "A spectrum of routing strategies for brain networks," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-24, March.

    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:421:y:2022:i:c:s0096300321009942. 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.