IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i9p932-d541214.html
   My bibliography  Save this article

Microscopic Numerical Simulations of Epidemic Models on Networks

Author

Listed:
  • Yutaka Okabe

    (Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan)

  • Akira Shudo

    (Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan)

Abstract

Mathematical models of the spread of epidemic diseases are studied, paying special attention to networks. We treat the Susceptible-Infected-Recovered (SIR) model and the Susceptible-Exposed-Infectious-Recovered (SEIR) model described by differential equations. We perform microscopic numerical simulations for corresponding epidemic models on networks. Comparing a random network and a scale-free network for the spread of the infection, we emphasize the role of hubs in a scale-free network. We also present a simple derivation of the exact solution of the SIR model.

Suggested Citation

  • Yutaka Okabe & Akira Shudo, 2021. "Microscopic Numerical Simulations of Epidemic Models on Networks," Mathematics, MDPI, vol. 9(9), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:932-:d:541214
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/9/932/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/9/932/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fernández-Villaverde, Jesús & Jones, Charles I., 2022. "Estimating and simulating a SIRD Model of COVID-19 for many countries, states, and cities," Journal of Economic Dynamics and Control, Elsevier, vol. 140(C).
    2. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    3. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    4. Anna D. Broido & Aaron Clauset, 2019. "Scale-free networks are rare," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    5. Andrew Atkeson, 2020. "What Will be the Economic Impact of COVID-19 in the US? Rough Estimates of Disease Scenarios," Staff Report 595, Federal Reserve Bank of Minneapolis.
    6. Ciro Cattuto & Wouter Van den Broeck & Alain Barrat & Vittoria Colizza & Jean-François Pinton & Alessandro Vespignani, 2010. "Dynamics of Person-to-Person Interactions from Distributed RFID Sensor Networks," PLOS ONE, Public Library of Science, vol. 5(7), pages 1-9, July.
    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. Rauf Ahmed Shams Malick & Syed Kashir Hasan & Fahad Samad & Nadeem Kafi Khan & Hassan Jamil Syed, 2023. "Smart Methods to Deal with COVID-19 at University-Level Institutions Using Social Network Analysis Techniques," Sustainability, MDPI, vol. 15(6), pages 1-17, March.

    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. Pongou, Roland & Tchuente, Guy & Tondji, Jean-Baptiste, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," GLO Discussion Paper Series 957, Global Labor Organization (GLO).
    2. Roland Pongou & Guy Tchuente & Jean-Baptiste Tondji, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," Papers 2110.10230, arXiv.org.
    3. Vinayak, & Raghuvanshi, Adarsh & kshitij, Avinash, 2023. "Signatures of capacity development through research collaborations in artificial intelligence and machine learning," Journal of Informetrics, Elsevier, vol. 17(1).
    4. Nicola Fuchs-Schündeln & Dirk Krueger & André Kurmann & Etienne Lalé & Alexander Ludwig & Irina Popova, 2023. "The Fiscal and Welfare Effects of Policy Responses to the Covid-19 School Closures," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 71(1), pages 35-98, March.
    5. Pablo D. Fajgelbaum & Amit Khandelwal & Wookun Kim & Cristiano Mantovani & Edouard Schaal, 2021. "Optimal Lockdown in a Commuting Network," American Economic Review: Insights, American Economic Association, vol. 3(4), pages 503-522, December.
    6. Elisa Giannone & Nuno Paixao & Xinle Pang, 2021. "The Geography of Pandemic Containment," Staff Working Papers 21-26, Bank of Canada.
    7. David Berger & Kyle Herkenhoff & Chengdai Huang & Simon Mongey, 2022. "Testing and Reopening in an SEIR Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 43, pages 1-21, January.
    8. Stefano Guarino & Enrico Mastrostefano & Massimo Bernaschi & Alessandro Celestini & Marco Cianfriglia & Davide Torre & Lena Rebecca Zastrow, 2021. "Inferring Urban Social Networks from Publicly Available Data," Future Internet, MDPI, vol. 13(5), pages 1-45, April.
    9. Harrison Hong & Neng Wang & Jinqiang Yang, 2020. "Implications of Stochastic Transmission Rates for Managing Pandemic Risks," NBER Working Papers 27218, National Bureau of Economic Research, Inc.
    10. Korolev, Ivan, 2021. "Identification and estimation of the SEIRD epidemic model for COVID-19," Journal of Econometrics, Elsevier, vol. 220(1), pages 63-85.
    11. Lin William Cong & Ke Tang & Bing Wang & Jingyuan Wang, 2021. "An AI-assisted Economic Model of Endogenous Mobility and Infectious Diseases: The Case of COVID-19 in the United States," Papers 2109.10009, arXiv.org.
    12. Pol Antràs & Stephen J. Redding & Esteban Rossi-Hansberg, 2023. "Globalization and Pandemics," American Economic Review, American Economic Association, vol. 113(4), pages 939-981, April.
    13. Alberto Bisin & Andrea Moro, 2020. "Learning Epidemiology by Doing: The Empirical Implications of a Spatial-SIR Model with Behavioral Responses," NBER Working Papers 27590, National Bureau of Economic Research, Inc.
    14. Getachew, Yoseph, 2020. "Optimal social distancing in SIR based macroeconomic models," MERIT Working Papers 2020-034, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    15. Lin Ma & Gil Shapira & Damien de Walque & Quy‐Toan Do & Jed Friedman & Andrei A. Levchenko, 2022. "The Intergenerational Mortality Trade‐Off Of Covid‐19 Lockdown Policies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(3), pages 1427-1468, August.
    16. Eichenbaum, Martin S. & Rebelo, Sergio & Trabandt, Mathias, 2022. "The macroeconomics of testing and quarantining," Journal of Economic Dynamics and Control, Elsevier, vol. 138(C).
    17. Garriga, Carlos & Manuelli, Rody & Sanghi, Siddhartha, 2022. "Optimal management of an epidemic: Lockdown, vaccine and value of life," Journal of Economic Dynamics and Control, Elsevier, vol. 140(C).
    18. Chernozhukov, Victor & Kasahara, Hiroyuki & Schrimpf, Paul, 2021. "Causal impact of masks, policies, behavior on early covid-19 pandemic in the U.S," Journal of Econometrics, Elsevier, vol. 220(1), pages 23-62.
    19. Lee, Sokbae & Liao, Yuan & Seo, Myung Hwan & Shin, Youngki, 2021. "Sparse HP filter: Finding kinks in the COVID-19 contact rate," Journal of Econometrics, Elsevier, vol. 220(1), pages 158-180.
    20. Glover, Andrew & Heathcote, Jonathan & Krueger, Dirk & Ríos-Rull, José-Víctor, 2023. "Health versus wealth: On the distributional effects of controlling a pandemic," Journal of Monetary Economics, Elsevier, vol. 140(C), pages 34-59.

    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:9:y:2021:i:9:p:932-:d:541214. 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.