Analysis of an Age-structured SIL model with demographics process and vertical transmission

Ramses Djidjou Demasse 1 Jean Jules Tewa 2 Samuel Bowong 3, 4
1 Department of Mathematics [Yaoundé]
2 ENSP - Ecole Nationale Supérieure Polytechnique [Yaoundé]
3 LIRIMA - Laboratoire International de Recherche en Informatique et Mathématiques Appliquées
4 Faculté des Sciences [Douala]
Résumé : We consider a mathematical SIL model for the spread of a directly transmitted infectious disease in an age-structured population; taking into account the demographic process and the vertical transmission of the disease. First we establish the mathematical well-posedness of the time evolution problem by using the semigroup approach. Next we prove that the basic reproduction ratio R0 is given as the spectral radius of a positive operator, and an endemic state exist if and only if the basic reproduction ratio R0 is greater than unity, while the disease-free equilibrium is locally asymptotically stable if R0<1. We also show that the endemic steady states are forwardly bifurcated from the disease-free steady state when R0 cross the unity. Finally we examine the conditions for the local stability of the endemic steady states.
Keywords : Age-structured model Semigroup Basic reproduction ratio Stability.
Type de document :
Article dans une revue
Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2014, 17, pp.23-52
Liste complète des métadonnées

Littérature citée [49 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-01300058
Contributeur : Coordination Episciences Iam <>
Soumis le : vendredi 8 avril 2016 - 16:09:45
Dernière modification le : mardi 24 avril 2018 - 13:33:28

Fichier

Vol.17.pp.23-52.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01300058, version 1

Collections

INSMI | LIRIMA | INRIA

Citation

Ramses Djidjou Demasse, Jean Jules Tewa, Samuel Bowong. Analysis of an Age-structured SIL model with demographics process and vertical transmission. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2014, 17, pp.23-52. 〈hal-01300058〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

160

Téléchargements de fichiers

199

Contact


archive-ouverte@inria.fr