Stability properties and Hopf bifurcation for a Hepatitis B infection model with exposed state and humoral immunity-response delay

Dayun Wu, Yongmei Su, Deshun Sun

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<R0, the infected equilibrium without immunity Q1is globally asymptotically stable. When R1> 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.

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Published: 2015-08-07

How to Cite this Article:

Dayun Wu, Yongmei Su, Deshun Sun, Stability properties and Hopf bifurcation for a Hepatitis B infection model with exposed state and humoral immunity-response delay, Communications in Mathematical Biology and Neuroscience, Vol 2015 (2015), Article ID 25

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.

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