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Microscopic Numerical Simulations of Epidemic Models on Networks

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. J. J. Esquivel-Gómez & J. G. Barajas-Ramírez, 2024. "Rapid disease spread on dense networks with power-law topology," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(5), pages 1-10, May.
    2. 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.

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