Math. Model. Nat. Phenom.
Volume 16, 2021
|Number of page(s)||32|
|Published online||03 November 2021|
Mathematical analysis of an age structured epidemic model with a quarantine class
Laboratoire d’Analyse Non linéaire et Mathématiques Appliquées, Département de Mathématiques, Université Aboubekr Belkaïd,
2 Institut de Mathématiques de Bordeaux, IMB UMR CNRS 5251, Université de Bordeaux, 33000, Bordeaux, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 1 October 2021
In this paper, an age structured epidemic Susceptible-Infected-Quarantined-Recovered-Infected (SIQRI) model is proposed, where we will focus on the role of individuals that leave the R-class before being completely recovered and thus will participate again to the disease transmission. We investigate the asymptotic behavior of solutions by studying the stability of both trivial and positive equilibria. In order to see the impact of the different model parameters like the relapse rate on the qualitative behavior of our system, we firstly, give an explicit expression of the basic reproduction number R0, which is a combination of the classical basic reproduction number for the SIQR model and some other model parameters, corresponding to the individuals infected by the relapsed ones. It will be shown that, if R0 ≤ 1, the disease free equilibrium is globally asymptotically stable and becomes unstable for R0 > 1. Secondly, while R0 > 1, a suitable Lyapunov functional is constructed to prove that the unique endemic equilibrium is globally asymptotically stable on some subset Ω0.
Mathematics Subject Classification: 58F15 / 58F17 / 53C35
Key words: Age structure / SIQRI model / relapse rate / global stability / persistence / basic reproductive number / Lyapunov functional
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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