Global asymptotic stability for a distributed delay differential-difference system of a Kermack-McKendrick SIR model - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Applicable Analysis Year : 2022

Global asymptotic stability for a distributed delay differential-difference system of a Kermack-McKendrick SIR model

Abstract

We investigate a system of distributed delay differential-difference equations describing an epidemic model of susceptible, infected, recovered and temporary protected population dynamics. A nonlocal term (distributed delay) appears in this model to describe the temporary protection period of the susceptible individuals. We investigate mathematical properties of the model. We obtain the global asymptotic stability of the two steady states: disease-free and endemic. We construct appropriate Lyapunov functionals where the basic reproduction number appears as a threshold for the global asymptotic behavior of the solution between disease extinction and persistence.
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Dates and versions

hal-03683861 , version 1 (01-06-2022)

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Mostafa Adimy, Abdennasser Chekroun, Toshikazu Kuniya. Global asymptotic stability for a distributed delay differential-difference system of a Kermack-McKendrick SIR model. Applicable Analysis, 2022, pp.1-13. ⟨10.1080/00036811.2022.2075352⟩. ⟨hal-03683861⟩
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