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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 12
130
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Research Article

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

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Pages 3463-3475 | Received 29 Sep 2021, Accepted 02 May 2022, Published online: 14 May 2022
 

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 the 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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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

A. Chekroun thanks grant, PRFU: C00L03UN220120180004, from DGRSDT of Algeria. T. Kuniya is supported by JSPS Grant-in-Aid for Early-Career Scientists [grant number 19K14594] and the Japan Agency for Medical Research and Development [grant number JP20fk0108535].

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