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An age-structured model for the transmission dynamics of hepatitis B: Asymptotic analysis

In this paper, we consider the age-structured model for the transmission dynamics of Hepatitis B virus (HBV) proposed earlier in the article by Zou et al.: An age-structured model for transmission dynamics of hepatitis B. SIAM J Appl Math 2010; 70: 3121-3139, where a slight modification is made. | Turk J Math (2017) 41: 436 – 460 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics http://journals.tubitak.gov.tr/math/ doi:10.3906/mat-1412-50 Research Article An age-structured model for the transmission dynamics of hepatitis B: asymptotic analysis 1 Rodrigue Yves M’PIKA MASSOUKOU1 , Aboubakari TRAORE2,∗ School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa 2 Department of Mathematics and Computer Sciences, Cheikh Anta Diop University, Dakar, Senegal Received: 20.12.2014 • Accepted/Published Online: 01.06.2016 • Final Version: 03.04.2017 Abstract: In this paper, we consider the age-structured model for the transmission dynamics of Hepatitis B virus (HBV) proposed earlier in the article by Zou et al.: An age-structured model for transmission dynamics of hepatitis B. SIAM J Appl Math 2010; 70: 3121-3139, where a slight modification is made. We consider that the HBV infection processes act on a time scale different from that of the vital processes. Such a model becomes a multiple time scale model and thus it often can be significantly simplified by various asymptotic methods. We apply, as in the paper of Banasiak and M’pika Massoukou: A singularly perturbed age structured SIRS model with fast recovery. Disc Cont Dyn Sys 2014, a suitable technique of asymptotic analysis, based on the Chapman–Enskog procedure, which allows separation of scales and aggregation of variables. Key words: Hepatitis B virus (HBV), age structure, asymptotic analysis 1. Introduction Hepatitis B virus (HBV) is mainly transmitted through body fluids like blood, semen, and vaginal secretions. One of the most important factors influencing the probability of developing carriage of HBV is age, involving mature individuals. Thus, it can be expected that the interplay of the demographic processes with the infection mechanism will produce a nontrivial dynamics. In this paper we consider the model for transmission dynamic of HBV introduced .