A mathematical model for hepatitis B with infection-age structure

Suxia  Zhang; Xiaxia  Xu

doi:10.3934/dcdsb.2016.21.1329

Article Contents

2016, Volume 21, Issue 4: 1329-1346. Doi: 10.3934/dcdsb.2016.21.1329

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A mathematical model for hepatitis B with infection-age structure

Suxia Zhang^1, and
Xiaxia Xu^1,

1.
School of Science, Xi'an University of Technology, Xi'an 710048

Received: February 2015

Revised: November 2015

Published: June 2016

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Abstract

A model with age of infection is formulated to study the possible effects of variable infectivity on HBV transmission dynamics. The stability of equilibria and persistence of the model are analyzed. The results show that if the basic reproductive number $\mathcal{R}_0<1$, then the disease-free equilibrium is globally asymptotically stable. For $\mathcal{R}_0>1$, the disease is uniformly persistent, and a Lyapunov function is used to show that the unique endemic equilibrium is globally stable in a special case.

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Mathematics Subject Classification: Primary: 92D25, 92D30; Secondary: 35B35, 37B25.

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