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

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 su...

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Bibliographic Details
Published in:Applicable analysis 2023-08, Vol.102 (12), p.3463-3475
Main Authors: Adimy, Mostafa, Chekroun, Abdennasser, Kuniya, Toshikazu
Format: Article
Language:English
Subjects:
Asymptotic properties
Delay
delay differential-difference system
Difference equations
Differential equations
Dynamical Systems
local and global asymptotic stability
Lyapunov-Krasovskii functional
Mathematics
SIR epidemic model
Stability
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Summary: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.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2022.2075352