| Volume 7, Number 2, 2017, Pages 532-553 DOI：10.11948/2017033 |
| Stability and bifurcation analysis of a viral infection model with delayed immune response |
| Hui Chen,Rui Xu |
| Keywords:Immunity time delay, thresholds, CTL immune response, Hopf bifurcation, global stability. |
| Abstract: |
| In this paper, we study a viral infection model with an immunity time delay accounting for the time between the immune system touching antigenic stimulation and generating CTLs. By calculation, we derive two thresholds to determine the global dynamics of the model, i.e., the reproduction number for viral infection $R_{0}$ and for CTL immune response $R_{1}$. By analyzing the characteristic equation, the local stability of each feasible equilibrium is discussed. Furthermore, the existence of Hopf bifurcation at the CTL-activated infection equilibrium is also studied. By constructing suitable Lyapunov functionals, we prove that when $R_{0}\leq1$, the infection-free equilibrium is globally asymptotically stable; when $R_{0}>1$ and $R_{1}\leq1$, the CTL-inactivated infection equilibrium is globally asymptotically stable; Numerical simulation is carried out to illustrate the main results in the end. |
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