Geodesic
Mathematical analysis of an age structured epidemic model with a quarantine class
Zakya Sari1 ; Tarik Mohammed Touaoula1 ; Bedreddine Ainseba2
1 Laboratoire d’Analyse Non linéaire et Mathématiques Appliquées, Département de Mathématiques, Université Aboubekr Belkaïd, Tlemcen 13000, Algérie.
2 Institut de Mathématiques de Bordeaux, IMB UMR CNRS 5251, Université de Bordeaux, 33000, Bordeaux, France.
Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 57 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/mmnp/2021049

Zakya Sari 1 ; Tarik Mohammed Touaoula 1 ; Bedreddine Ainseba 2

1 Laboratoire d’Analyse Non linéaire et Mathématiques Appliquées, Département de Mathématiques, Université Aboubekr Belkaïd, Tlemcen 13000, Algérie.
2 Institut de Mathématiques de Bordeaux, IMB UMR CNRS 5251, Université de Bordeaux, 33000, Bordeaux, France. 
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Zakya Sari; Tarik Mohammed Touaoula; Bedreddine Ainseba. Mathematical analysis of an age structured epidemic model with a quarantine class. Mathematical modelling of natural phenomena, Tome 16 (2021), article  no. 57. doi: 10.1051/mmnp/2021049

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