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An Epidemic Model with Time Delay Determined by the Disease Duration

Author

Listed:
  • Samiran Ghosh

    (Department of Mathematics and Statistics, IIT Kanpur, Kanpur 208016, India
    These authors contributed equally to this work.)

  • Vitaly Volpert

    (Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
    Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia
    These authors contributed equally to this work.)

  • Malay Banerjee

    (Department of Mathematics and Statistics, IIT Kanpur, Kanpur 208016, India
    These authors contributed equally to this work.)

Abstract

Immuno-epidemiological models with distributed recovery and death rates can describe the epidemic progression more precisely than conventional compartmental models. However, the required immunological data to estimate the distributed recovery and death rates are not easily available. An epidemic model with time delay is derived from the previously developed model with distributed recovery and death rates, which does not require precise immunological data. The resulting generic model describes epidemic progression using two parameters, disease transmission rate and disease duration. The disease duration is incorporated as a delay parameter. Various epidemic characteristics of the delay model, namely the basic reproduction number, the maximal number of infected, and the final size of the epidemic are derived. The estimation of disease duration is studied with the help of real data for COVID-19. The delay model gives a good approximation of the COVID-19 data and of the more detailed model with distributed parameters.

Suggested Citation

  • Samiran Ghosh & Vitaly Volpert & Malay Banerjee, 2022. "An Epidemic Model with Time Delay Determined by the Disease Duration," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2561-:d:869361
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    References listed on IDEAS

    as
    1. Khan, Muhammad Altaf & Atangana, Abdon, 2022. "Mathematical modeling and analysis of COVID-19: A study of new variant Omicron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    2. d’Onofrio, Alberto & Banerjee, Malay & Manfredi, Piero, 2020. "Spatial behavioural responses to the spread of an infectious disease can suppress Turing and Turing–Hopf patterning of the disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
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    Cited by:

    1. Vladica S. Stojanović & Hassan S. Bakouch & Eugen Ljajko & Najla Qarmalah, 2023. "Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    2. Masoud Saade & Sebastian Aniţa & Vitaly Volpert, 2023. "Dynamics of Persistent Epidemic and Optimal Control of Vaccination," Mathematics, MDPI, vol. 11(17), pages 1-15, September.
    3. Mihailo Jovanović & Vladica Stojanović & Kristijan Kuk & Brankica Popović & Petar Čisar, 2022. "Asymptotic Properties and Application of GSB Process: A Case Study of the COVID-19 Dynamics in Serbia," Mathematics, MDPI, vol. 10(20), pages 1-28, October.

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