Global dynamics of a differential-difference system: a case of Kermack-McKendrick SIR model with age-structured protection phase

Autor(es)

Adimy, Mostafa ^[1] ; Chekroun, Abdennasser ^[2] ; Ferreira, Claudia Pio ^[3]

Afiliação do(s) autor(es)

^[1] Univ Lyon 1, Inst Camille Jordan, CNRS UMR 5208, INRIA, F-69200 Villeurbanne - France

^[2] Univ Tlemcen, Lab Anal Nonlineaire & Math Appl, Tilimsen 13000 - Algeria

^[3] Sao Paulo State Univ, UNESP, Dept Biostat, BR-18618689 Botucatu, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Mathematical Biosciences and Engineering; v. 17, n. 2, p. 1329-1354, 2020.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 18/24058-1 - Arboviroses: dinâmica e controle de vetores
• Beneficiário: Cláudia Pio Ferreira
• Modalidade de apoio: Auxílio à Pesquisa - Regular