IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i14p2217-d1435869.html
   My bibliography  Save this article

Sensitivity Analysis and Uncertainty of a Myocardial Infarction Model

Author

Listed:
  • Benito Chen-Charpentier

    (Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
    These authors contributed equally to this work.)

  • Hristo Kojouharov

    (Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
    These authors contributed equally to this work.)

Abstract

There is uncertainty in the results of any mathematical model due to different reasons. It is important to estimate this uncertainty. Sensitivity analysis is commonly used to estimate how the changes in the input parameters affect the solutions of the model. In this paper, we discuss different ways of performing local and global sensitivity analyses and apply them to two models: an epidemic model and a new myocardial infarction model, both based on ordinary differential equations. The first model is a simple model used to explain the ideas, while the second one shows how to apply them to a model with more state variables and parameters. We find that if the parameters are not accurately known, local sensitivity analysis can be misleading and that global sensitivity methods that sample the whole parameter space, varying all the values of the parameters at the same time, are the most reliable. We also show how the sensitivity analysis results can be used to determine the uncertainty in the results of the model. We present numerical simulations.

Suggested Citation

  • Benito Chen-Charpentier & Hristo Kojouharov, 2024. "Sensitivity Analysis and Uncertainty of a Myocardial Infarction Model," Mathematics, MDPI, vol. 12(14), pages 1-25, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2217-:d:1435869
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/14/2217/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/14/2217/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. H. Christopher Frey & Sumeet R. Patil, 2002. "Identification and Review of Sensitivity Analysis Methods," Risk Analysis, John Wiley & Sons, vol. 22(3), pages 553-578, June.
    2. Chuan Qin & Yuqing Jin & Meng Tian & Ping Ju & Shun Zhou, 2023. "Comparative Study of Global Sensitivity Analysis and Local Sensitivity Analysis in Power System Parameter Identification," Energies, MDPI, vol. 16(16), pages 1-21, August.
    3. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    4. Vittoria Colizza & Alain Barrat & Marc Barthelemy & Alain-Jacques Valleron & Alessandro Vespignani, 2007. "Modeling the Worldwide Spread of Pandemic Influenza: Baseline Case and Containment Interventions," PLOS Medicine, Public Library of Science, vol. 4(1), pages 1-16, January.
    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. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
    2. Emanuele Borgonovo & Gordon B. Hazen & Elmar Plischke, 2016. "A Common Rationale for Global Sensitivity Measures and Their Estimation," Risk Analysis, John Wiley & Sons, vol. 36(10), pages 1871-1895, October.
    3. Luigi Dolores & Maria Macchiaroli & Gianluigi De Mare, 2022. "Financial Impacts of the Energy Transition in Housing," Sustainability, MDPI, vol. 14(9), pages 1-17, April.
    4. Sinan Xiao & Zhenzhou Lu & Pan Wang, 2018. "Multivariate Global Sensitivity Analysis Based on Distance Components Decomposition," Risk Analysis, John Wiley & Sons, vol. 38(12), pages 2703-2721, December.
    5. Andreas Binder & Onkar Jadhav & Volker Mehrmann, 2021. "Error Analysis of a Model Order Reduction Framework for Financial Risk Analysis," Papers 2110.00774, arXiv.org.
    6. Isadora Antoniano‐Villalobos & Emanuele Borgonovo & Sumeda Siriwardena, 2018. "Which Parameters Are Important? Differential Importance Under Uncertainty," Risk Analysis, John Wiley & Sons, vol. 38(11), pages 2459-2477, November.
    7. Tatsuya Sakurahara & Seyed Reihani & Ernie Kee & Zahra Mohaghegh, 2020. "Global importance measure methodology for integrated probabilistic risk assessment," Journal of Risk and Reliability, , vol. 234(2), pages 377-396, April.
    8. João R. B. Paiva & Alana S. Magalhães & Pedro H. F. Moraes & Júnio S. Bulhões & Wesley P. Calixto, 2021. "Stability Metric Based on Sensitivity Analysis Applied to Electrical Repowering System," Energies, MDPI, vol. 14(22), pages 1-21, November.
    9. Tarafdar, Anirban & Majumder, P. & Deb, Madhujit & Bera, U.K., 2023. "Application of a q-rung orthopair hesitant fuzzy aggregated Type-3 fuzzy logic in the characterization of performance-emission profile of a single cylinder CI-engine operating with hydrogen in dual fu," Energy, Elsevier, vol. 269(C).
    10. Vincenzo Varriale & Antonello Cammarano & Francesca Michelino & Mauro Caputo, 2021. "Sustainable Supply Chains with Blockchain, IoT and RFID: A Simulation on Order Management," Sustainability, MDPI, vol. 13(11), pages 1-23, June.
    11. S. M. Mniszewski & S. Y. Del Valle & P. D. Stroud & J. M. Riese & S. J. Sydoriak, 2008. "Pandemic simulation of antivirals + school closures: buying time until strain-specific vaccine is available," Computational and Mathematical Organization Theory, Springer, vol. 14(3), pages 209-221, September.
    12. Floriana Gargiulo & Sônia Ternes & Sylvie Huet & Guillaume Deffuant, 2010. "An Iterative Approach for Generating Statistically Realistic Populations of Households," PLOS ONE, Public Library of Science, vol. 5(1), pages 1-9, January.
    13. S. Cucurachi & E. Borgonovo & R. Heijungs, 2016. "A Protocol for the Global Sensitivity Analysis of Impact Assessment Models in Life Cycle Assessment," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 357-377, February.
    14. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    15. Teruhiko Yoneyama & Sanmay Das & Mukkai Krishnamoorthy, 2012. "A Hybrid Model for Disease Spread and an Application to the SARS Pandemic," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 15(1), pages 1-5.
    16. Wen Shi & Xi Chen & Jennifer Shang, 2019. "An Efficient Morris Method-Based Framework for Simulation Factor Screening," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 745-770, October.
    17. F. Wang & G. H. Huang & Y. Fan & Y. P. Li, 2020. "Robust Subsampling ANOVA Methods for Sensitivity Analysis of Water Resource and Environmental Models," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(10), pages 3199-3217, August.
    18. Daniel Harenberg & Stefano Marelli & Bruno Sudret & Viktor Winschel, 2019. "Uncertainty quantification and global sensitivity analysis for economic models," Quantitative Economics, Econometric Society, vol. 10(1), pages 1-41, January.
    19. Tobias Fissler & Silvana M. Pesenti, 2022. "Sensitivity Measures Based on Scoring Functions," Papers 2203.00460, arXiv.org, revised Jul 2022.
    20. Shang, Xiaobing & Su, Li & Fang, Hai & Zeng, Bowen & Zhang, Zhi, 2023. "An efficient multi-fidelity Kriging surrogate model-based method for global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 229(C).

    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:12:y:2024:i:14:p:2217-:d:1435869. 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.