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Modeling epidemics through ladder operators

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  • Bagarello, F.
  • Gargano, F.
  • Roccati, F.

Abstract

We propose a simple model of spreading of some infection in an originally healthy population which is different from other models existing in the literature. In particular, we use an operator technique which allows us to describe in a natural way the possible interactions between healthy and un-healthy populations, and their transformation into recovered and to dead people. After a rather general discussion, we apply our method to the analysis of Chinese data for the SARS-2003 (Severe acute respiratory syndrome; SARS-CoV-1) and the Coronavirus COVID-19 (Corona Virus Disease; SARS-CoV-2) and we show that the model works very well in reproducing the long-time behaviour of the disease, and in particular in finding the number of affected and dead people in the limit of large time. Moreover, we show how the model can be easily modified to consider some lockdown measure, and we deduce that this procedure drastically reduces the asymptotic value of infected individuals, as expected, and observed in real life.

Suggested Citation

  • Bagarello, F. & Gargano, F. & Roccati, F., 2020. "Modeling epidemics through ladder operators," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305890
    DOI: 10.1016/j.chaos.2020.110193
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    References listed on IDEAS

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    1. Arora, Parul & Kumar, Himanshu & Panigrahi, Bijaya Ketan, 2020. "Prediction and analysis of COVID-19 positive cases using deep learning models: A descriptive case study of India," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Bagarello, F., 2020. "One-directional quantum mechanical dynamics and an application to decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Steffen Unkel & C. Paddy Farrington & Paul H. Garthwaite & Chris Robertson & Nick Andrews, 2012. "Statistical methods for the prospective detection of infectious disease outbreaks: a review," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 175(1), pages 49-82, January.
    4. Bagarello,Fabio, 2019. "Quantum Concepts in the Social, Ecological and Biological Sciences," Cambridge Books, Cambridge University Press, number 9781108492126, October.
    5. David A Rasmussen & Oliver Ratmann & Katia Koelle, 2011. "Inference for Nonlinear Epidemiological Models Using Genealogies and Time Series," PLOS Computational Biology, Public Library of Science, vol. 7(8), pages 1-11, August.
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    1. Giovanni Nastasi & Carla Perrone & Salvatore Taffara & Giorgia Vitanza, 2022. "A Time-Delayed Deterministic Model for the Spread of COVID-19 with Calibration on a Real Dataset," Mathematics, MDPI, vol. 10(4), pages 1-14, February.

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