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Updated: Dec 25, 2025

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Global dynamics of a differential-difference system: a case of Kermack-McKendrick SIR model with age-structured
Mostafa Adimy1, Abdennasser Chekroun2, Claudia Pio Ferreira3
1Inria, CNRS UMR 5208, Institut Camille Jordan, Université Lyon 1, F-69200 - Villeurbanne, France.
Abstract:
In this paper, we are concerned with an epidemic model of susceptible, infected and recovered (SIR) population dynamic by considering an age-structured phase of protection with limited duration, for instance due to vaccination or drugs with temporary immunity. The model is reduced to a delay differential-difference system, where the delay is the duration of the protection phase. We investigate the local asymptotic stability of the two steady states: disease-free and endemic. We also establish when the endemic steady state exists, the uniform persistence of the disease. We construct quadratic and logarithmic Lyapunov functions to establish the global asymptotic stability of the two steady states. We prove that the global stability is completely determined by the basic reproduction number.
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