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Extending the SIR epidemic model

Author

Listed:
  • Satsuma, J
  • Willox, R
  • Ramani, A
  • Grammaticos, B
  • Carstea, A.S

Abstract

We investigate possible extensions of the susceptible–infective-removed (SIR) epidemic model. We show that there exists a large class of functions representing interaction between the susceptible and infective populations for which the model has a realistic behaviour and preserves the essential features of the classical SIR model. We also present a new discretisation of the SIR model which has the advantage of possessing a conserved quantity, thus making possible the estimation of the non-infected population at the end of the epidemic. A cellular automaton SIR is also constructed on the basis of the discrete-time system.

Suggested Citation

  • Satsuma, J & Willox, R & Ramani, A & Grammaticos, B & Carstea, A.S, 2004. "Extending the SIR epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 369-375.
    • Handle: RePEc:eee:phsmap:v:336:y:2004:i:3:p:369-375
    DOI: 10.1016/j.physa.2003.12.035
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    Citations

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    Cited by:

    1. Alexander Chudik & M. Hashem Pesaran & Alessandro Rebucci, 2023. "Social Distancing, Vaccination and Evolution of COVID-19 Transmission Rates in Europe," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 71(2), pages 474-508, June.
    2. Hu, Zengyun & Teng, Zhidong & Zhang, Tailei & Zhou, Qiming & Chen, Xi, 2017. "Globally asymptotically stable analysis in a discrete time eco-epidemiological system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 20-31.
    3. Narisa Zhao & Hui Li, 2020. "How can social commerce be boosted? The impact of consumer behaviors on the information dissemination mechanism in a social commerce network," Electronic Commerce Research, Springer, vol. 20(4), pages 833-856, December.
    4. Alexander Chudik & M. Hashem Pesaran & Alessandro Rebucci, 2020. "Voluntary and Mandatory Social Distancing: Evidence on COVID-19 Exposure Rates from Chinese Provinces and Selected Countries," Globalization Institute Working Papers 382, Federal Reserve Bank of Dallas.
    5. Zaman, Gul & Kang, Yong Han & Cho, Giphil & Jung, Il Hyo, 2017. "Optimal strategy of vaccination & treatment in an SIR epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 63-77.
    6. Alexander Chudik & M. Hashem Pesaran & Alessandro Rebucci, 2021. "COVID-19 Time-Varying Reproduction Numbers Worldwide: An Empirical Analysis of Mandatory and Voluntary Social Distancing," Globalization Institute Working Papers 407, Federal Reserve Bank of Dallas.
    7. Wang, Xingyuan & Zhao, Tianfang & Qin, Xiaomeng, 2016. "Model of epidemic control based on quarantine and message delivery," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 168-178.
    8. Joost R. Santos & Lucia Castro Herrera & Krista Danielle S. Yu & Sheree Ann T. Pagsuyoin & Raymond R. Tan, 2014. "State of the Art in Risk Analysis of Workforce Criticality Influencing Disaster Preparedness for Interdependent Systems," Risk Analysis, John Wiley & Sons, vol. 34(6), pages 1056-1068, June.
    9. Pelayo Martínez-Fernández & Zulima Fernández-Muñiz & Ana Cernea & Juan Luis Fernández-Martínez & Andrzej Kloczkowski, 2023. "Three Mathematical Models for COVID-19 Prediction," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    10. Fu, Libi & Song, Weiguo & Lv, Wei & Lo, Siuming, 2014. "Simulation of emotional contagion using modified SIR model: A cellular automaton approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 380-391.
    11. Awawdeh, Fadi & Adawi, A. & Mustafa, Z., 2009. "Solutions of the SIR models of epidemics using HAM," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3047-3052.
    12. Cuñat, Alejandro & Zymek, Robert, 2022. "The (structural) gravity of epidemics," European Economic Review, Elsevier, vol. 144(C).
    13. Nian, Fuzhong & Liu, Jinshuo, 2021. "Feedback driven message spreading on network," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).

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