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Delays and Exposed Populations in Infection Models

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  • Benito Chen-Charpentier

    (Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA)

Abstract

Most biological processes take time to occur. In infectious diseases, such as malaria or chikungunya, there is a period of time between when a susceptible individual gets bitten by the vector, and when the individual develops the disease. These times are commonly modeled by introducing delays or by adding exposed as a new population class. Given a model based on differential equations, delays can be introduced in different forms. In this paper, we study different ways of introducing the delays and, alternatively, using exposed populations. We also analyze their steady solutions and stability, and establish the conditions under which the studied models predict an epidemic. Results and conclusions are presented.

Suggested Citation

  • Benito Chen-Charpentier, 2023. "Delays and Exposed Populations in Infection Models," Mathematics, MDPI, vol. 11(8), pages 1-22, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1919-:d:1127118
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    References listed on IDEAS

    as
    1. Miranda Chan & Michael A Johansson, 2012. "The Incubation Periods of Dengue Viruses," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-7, November.
    2. Bellen, Alfredo & Zennaro, Marino, 2013. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780199671373, Decembrie.
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    Cited by:

    1. Halet Ismail & Amar Debbouche & Soundararajan Hariharan & Lingeshwaran Shangerganesh & Stanislava V. Kashtanova, 2024. "Stability and Optimality Criteria for an SVIR Epidemic Model with Numerical Simulation," Mathematics, MDPI, vol. 12(20), pages 1-29, October.
    2. Calatayud, Julia & Jornet, Marc & Pinto, Carla M.A., 2024. "On the interpretation of Caputo fractional compartmental models," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. Julio C. Miranda & Abraham J. Arenas & Gilberto González-Parra & Luis Miguel Villada, 2024. "Existence of Traveling Waves of a Diffusive Susceptible–Infected–Symptomatic–Recovered Epidemic Model with Temporal Delay," Mathematics, MDPI, vol. 12(5), pages 1-36, February.

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