https://doi.org/10.1140/epjp/s13360-024-05764-1
Regular Article
Stability and Hopf bifurcation of a HBV infection model with capsids and CTL immune response delay
1
School of Mathematics and Physics, HNP-LAMA, Hunan University of Arts and Science, 415000, Changde, Hunan, People’s Republic of China
2
School of Mathematics and Statistics, HNP-LAMA, Central South University, 410083, Changsha, Hunan, People’s Republic of China
Received:
21
July
2024
Accepted:
19
October
2024
Published online:
4
November
2024
In this paper, an in-host HBV model with two infection routes including cell-virus infection and cell-cell infection, intracellular delay 
, virus replication delay 
and CTL immune response delay 
are investigated. Firstly, the positivity and boundedness of all solutions for the model with nonnegative initial values have been established. Next, two key parameters with significant biological importance, the virus reproductive number 
and the CTL immune reproductive number 
, are derived. Subsequently, the stability of equilibria is analyzed by constructing appropriate Lyapunov functionals and applying LaSalle’s invariance principle. The results indicate that intracellular delay and virus replication delay do not affect the stability of the three equilibria. However, a positive CTL immune response delay can lead to stability switches at the endemic equilibrium. By treating the CTL immune response delay as a bifurcation parameter, certain conditions for these stability switches are determined. It is concluded that as the CTL immune response delay increases, the endemic equilibrium becomes unstable, resulting in a Hopf bifurcation in the system. Finally, numerical simulations further validate the theoretical findings.
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