IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i10p2321-d1148280.html
   My bibliography  Save this article

Bias Due to Averaging the Logistic and SI Models

Author

Listed:
  • Dorothy I. Wallace

    (Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA)

Abstract

Modelers have choices in how they approach a problem, with different approaches potentially leading to different outcomes. Sometimes one approach gives a consistently lower (or higher) result than another. The theorem and corollaries in this study show that if the logistic equation or, equivalently, the SI model, are perturbed at time zero by a range of values with mean zero, the resulting trajectories must average to a value below (for logistic and I) or above (for S) the solution with average initial condition. The proof of the theorem shows that this phenomenon is the result of algebraic properties of the nonlinear quadratic term, although we note it can be extended to a larger class of systems. More importantly it shows that the only necessary criterion is that the perturbations average to zero. The source of them and the properties of their distribution does not matter to the result of the theorem but does affect the magnitude of the proven difference.

Suggested Citation

  • Dorothy I. Wallace, 2023. "Bias Due to Averaging the Logistic and SI Models," Mathematics, MDPI, vol. 11(10), pages 1-8, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2321-:d:1148280
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/10/2321/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/10/2321/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hazhir Rahmandad & John Sterman, 2008. "Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models," Management Science, INFORMS, vol. 54(5), pages 998-1014, May.
    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. Lewe, J.-H. & Hivin, L.F. & Mavris, D.N., 2014. "A multi-paradigm approach to system dynamics modeling of intercity transportation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 188-202.
    2. 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.
    3. 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.
    4. Cowan, Kelly R. & Daim, Tugrul U., 2011. "Review of technology acquisition and adoption research in the energy sector," Technology in Society, Elsevier, vol. 33(3), pages 183-199.
    5. Lu, Xuefei & Borgonovo, Emanuele, 2023. "Global sensitivity analysis in epidemiological modeling," European Journal of Operational Research, Elsevier, vol. 304(1), pages 9-24.
    6. Nguyen, Le Khanh Ngan & Howick, Susan & Megiddo, Itamar, 2024. "A framework for conceptualising hybrid system dynamics and agent-based simulation models," European Journal of Operational Research, Elsevier, vol. 315(3), pages 1153-1166.
    7. Santos, Mário & Bastos, Rita & Cabral, João Alexandre, 2013. "Converting conventional ecological datasets in dynamic and dynamic spatially explicit simulations: Current advances and future applications of the Stochastic Dynamic Methodology (StDM)," Ecological Modelling, Elsevier, vol. 258(C), pages 91-100.
    8. Wouter Vermeer & Otto Koppius & Peter Vervest, 2018. "The Radiation-Transmission-Reception (RTR) model of propagation: Implications for the effectiveness of network interventions," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-21, December.
    9. Lei Xu & Ronggui Ding & Lei Wang, 2022. "How to facilitate knowledge diffusion in collaborative innovation projects by adjusting network density and project roles," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(3), pages 1353-1379, March.
    10. Jan Kwakkel & Willem Auping, 2021. "Reaction: A commentary on Lustick and Tetlock (2021)," Futures & Foresight Science, John Wiley & Sons, vol. 3(2), June.
    11. Tesfatsion, Leigh, 2017. "Modeling Economic Systems as Locally-Constructive Sequential Games," ISU General Staff Papers 201704300700001022, Iowa State University, Department of Economics.
    12. 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).
    13. Lixin Zhou & Jie Lin & Yanfeng Li & Zhenyu Zhang, 2020. "Innovation Diffusion of Mobile Applications in Social Networks: A Multi-Agent System," Sustainability, MDPI, vol. 12(7), pages 1-17, April.
    14. Amini, Mehdi & Wakolbinger, Tina & Racer, Michael & Nejad, Mohammad G., 2012. "Alternative supply chain production–sales policies for new product diffusion: An agent-based modeling and simulation approach," European Journal of Operational Research, Elsevier, vol. 216(2), pages 301-311.
    15. Teglio, Andrea, 2020. "On the typicality of the representative agent," MPRA Paper 105407, University Library of Munich, Germany.
    16. Rixen, Martin & Weigand, Jürgen, 2014. "Agent-based simulation of policy induced diffusion of smart meters," Technological Forecasting and Social Change, Elsevier, vol. 85(C), pages 153-167.
    17. Yu Zhao & Shaopeng Wei & Yu Guo & Qing Yang & Xingyan Chen & Qing Li & Fuzhen Zhuang & Ji Liu & Gang Kou, 2022. "Combining Intra-Risk and Contagion Risk for Enterprise Bankruptcy Prediction Using Graph Neural Networks," Papers 2202.03874, arXiv.org, revised Jul 2022.
    18. Hai-hua Hu & Jun Lin & Wen-tian Cui, 2015. "Intervention Strategies and the Diffusion of Collective Behavior," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 18(3), pages 1-16.
    19. Matthew Oremland & Reinhard Laubenbacher, 2014. "Using difference equations to find optimal tax structures on the SugarScape," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(2), pages 233-253, October.
    20. Laciana, Carlos E. & Rovere, Santiago L. & Podestá, Guillermo P., 2013. "Exploring associations between micro-level models of innovation diffusion and emerging macro-level adoption patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1873-1884.

    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:gam:jmathe:v:11:y:2023:i:10:p:2321-:d:1148280. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.