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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

A mathematical model for hepatitis B with infection-age structure

Pages: 1329 - 1346, Volume 21, Issue 4, June 2016      doi:10.3934/dcdsb.2016.21.1329

 
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Suxia Zhang - School of Science, Xi'an University of Technology, Xi'an 710048, China (email)
Xiaxia Xu - School of Science, Xi'an University of Technology, Xi'an 710048, China (email)

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.

Keywords:  Mathematical model, hepatitis B, age of infection, stability, uniform persistence.
Mathematics Subject Classification:  Primary: 92D25, 92D30; Secondary: 35B35, 37B25.

Received: February 2015;      Revised: November 2015;      Available Online: March 2016.

 References