Stability properties and Hopf bifurcation for a Hepatitis B infection model with exposed state and humoral immunity-response delay
Abstract
In this paper, a dynamics behavior of a delayed hepatitis B infection model with exposed state and humoral immunity is studied. The basic reproductive number R0and humoral immune reproductive number R1are introduced. By using suitable Lyapunov functional and LaSalle invariant principle, it is proved that when R0< 1, the infection-free equilibrium Q0is globally asymptotically stable; if R1<1 1, the sufficient conditions to the local stability of the infected equilibrium with immunity Q2can be obtained. The time delay can change the stability of Q2and lead to the existence of Hopf bifurcations. The stabilities of periodic solutions are also investigated. Finally, numerical simulations are carried out.
- Published
- 7 August 2015
- Volume
- 2015 (2015)
- License
- CC BY 3.0
Copyright © 2015 Dayun Wu, Yongmei Su, Deshun Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
D. Wu, Y. Su, D. Sun, Stability properties and Hopf bifurcation for a Hepatitis B infection model with exposed state and humoral immunity-response delay, Commun. Math. Biol. Neurosci. 2015 (2015), 25.
BibTeX
@article{Wu2015,
author = {Wu, Dayun and Su, Yongmei and Sun, Deshun},
title = {Stability properties and Hopf bifurcation for a Hepatitis B infection model with exposed state and humoral immunity-response delay},
journal = {Commun. Math. Biol. Neurosci.},
volume = {2015},
year = {2015},
pages = {25},
doi = {}
}