IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v617y2023ics0378437123001681.html
   My bibliography  Save this article

Weibull dynamics and power-law diffusion of epidemics in small world 2D networks

Author

Listed:
  • Xenikos, D.G.
  • Constantoudis, V.

Abstract

We demonstrate that the Weibull statistics characterize the time dependence of the epidemic spread in several idealized cases on 2-D Cartesian lattices, with and without small world structure. These cases include infection from nearest and next nearest neighbors; infection from long-distant neighbors; infection due to external influence. The Weibull closed form for the aggregated disease propagation is used as an analytic tool to elucidate the effect of small world topology in the diffusion scaling. It may be also used to formalize and contain the extensive diversity of real life cases. Along these lines, besides the straightforward implementation of the studied cases in epidemiology, our work proposes a power-law scaling in the Bass model for applications in the diffusion of the technological innovation.

Suggested Citation

  • Xenikos, D.G. & Constantoudis, V., 2023. "Weibull dynamics and power-law diffusion of epidemics in small world 2D networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    • Handle: RePEc:eee:phsmap:v:617:y:2023:i:c:s0378437123001681
    DOI: 10.1016/j.physa.2023.128613
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123001681
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2023.128613?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. Elmar Kiesling & Markus Günther & Christian Stummer & Lea Wakolbinger, 2012. "Agent-based simulation of innovation diffusion: a review," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 183-230, June.
    2. Fibich, Gadi & Levin, Tomer, 2020. "Percolation of new products," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Stauffer, D. & Jan, N., 2000. "Sharp peaks in the percolation model for stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 215-219.
    4. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
    5. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    6. Antonio Barrera & Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic," Mathematics, MDPI, vol. 9(19), pages 1-29, September.
    7. Goldenberg, J & Libai, B & Solomon, S & Jan, N & Stauffer, D, 2000. "Marketing percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 335-347.
    8. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.
    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. Abedi, Vahideh Sadat, 2019. "Compartmental diffusion modeling: Describing customer heterogeneity & communication network to support decisions for new product introductions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    2. Palmer, J. & Sorda, G. & Madlener, R., 2015. "Modeling the diffusion of residential photovoltaic systems in Italy: An agent-based simulation," Technological Forecasting and Social Change, Elsevier, vol. 99(C), pages 106-131.
    3. Zhang, Cen & Schmöcker, Jan-Dirk & Kuwahara, Masahiro & Nakamura, Toshiyuki & Uno, Nobuhiro, 2020. "A diffusion model for estimating adoption patterns of a one-way carsharing system in its initial years," Transportation Research Part A: Policy and Practice, Elsevier, vol. 136(C), pages 135-150.
    4. Chumnumpan, Pattarin & Shi, Xiaohui, 2019. "Understanding new products’ market performance using Google Trends," Australasian marketing journal, Elsevier, vol. 27(2), pages 91-103.
    5. Byrka, Katarzyna & Jȩdrzejewski, Arkadiusz & Sznajd-Weron, Katarzyna & Weron, Rafał, 2016. "Difficulty is critical: The importance of social factors in modeling diffusion of green products and practices," Renewable and Sustainable Energy Reviews, Elsevier, vol. 62(C), pages 723-735.
    6. Shi, Xiaohui & Chumnumpan, Pattarin, 2019. "Modelling market dynamics of multi-brand and multi-generational products," European Journal of Operational Research, Elsevier, vol. 279(1), pages 199-210.
    7. Konstantinos Petridis & Nikolaos E. Petridis, 2022. "Diffusion of Innovations in Middle Eastern versus Western Markets: A Mathematical Computation Cellular Automata Simulation Model," Operational Research, Springer, vol. 22(2), pages 1597-1616, April.
    8. Sebastiano A. Delre & Wander Jager & Marco A. Janssen, 2007. "Diffusion dynamics in small-world networks with heterogeneous consumers," Computational and Mathematical Organization Theory, Springer, vol. 13(2), pages 185-202, June.
    9. Elmar Kiesling & Markus Günther & Christian Stummer & Lea Wakolbinger, 2012. "Agent-based simulation of innovation diffusion: a review," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 183-230, June.
    10. Karakaya, Emrah, 2014. "Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems," INDEK Working Paper Series 2014/6, Royal Institute of Technology, Department of Industrial Economics and Management.
    11. Hüseyin İkizler, 2019. "Contagion of network products in small-world networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(4), pages 789-809, December.
    12. Javaid, Aneeque & Janssen, Marco A. & Reuter, Hauke & Schlüter, Achim, 2017. "When Patience Leads to Destruction: The Curious Case of Individual Time Preferences and the Adoption of Destructive Fishing Gears," Ecological Economics, Elsevier, vol. 142(C), pages 91-103.
    13. Baburin, Vyacheslav & Zemtsov, Stepan, 2014. "Diffussion of ICT-products and "five Russias"," MPRA Paper 68926, University Library of Munich, Germany, revised 10 May 2014.
    14. Xiao, Yu & Han, Jingti, 2016. "Forecasting new product diffusion with agent-based models," Technological Forecasting and Social Change, Elsevier, vol. 105(C), pages 167-178.
    15. Meihan He & Jongsu Lee, 2020. "Social culture and innovation diffusion: a theoretically founded agent-based model," Journal of Evolutionary Economics, Springer, vol. 30(4), pages 1109-1149, September.
    16. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    17. Constanza Fosco, 2012. "Spatial Difusion and Commuting Flows," Documentos de Trabajo en Economia y Ciencia Regional 30, Universidad Catolica del Norte, Chile, Department of Economics, revised Sep 2012.
    18. Peres, Renana & Muller, Eitan & Mahajan, Vijay, 2010. "Innovation diffusion and new product growth models: A critical review and research directions," International Journal of Research in Marketing, Elsevier, vol. 27(2), pages 91-106.
    19. Kivi, Antero & Smura, Timo & Töyli, Juuso, 2012. "Technology product evolution and the diffusion of new product features," Technological Forecasting and Social Change, Elsevier, vol. 79(1), pages 107-126.
    20. Al-Alawi, Baha M. & Bradley, Thomas H., 2013. "Review of hybrid, plug-in hybrid, and electric vehicle market modeling Studies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 21(C), pages 190-203.

    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:phsmap:v:617:y:2023:i:c:s0378437123001681. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.