| Abstract: |
| In this joint work with Xuejun Pan and Professor Hongying Shu, we investigate the impact of time delay in CTL immune response on an HTLV-I infection model. We use the basic reproduction number for viral infection $R_0$ and the basic reproduction number for CTL response $R_{CTL}$ to characterize the model dynamics. In particular, we obtain the global dynamics if $R_0\le 1$ or $R_{CTL}\le11$.
However, the model dynamics become much rich when $R_{CTL}>1$.
In this case, we use the time delay as a bifurcation parameter to obtain stability switch result on the positive equilibrium and global bifurcation diagrams for the model system.
We also conduct higher-order normal form analysis and apply center manifold theory to classify the rich model dynamics near the double Hopf bifurcation points.
Our analysis indicates that time delay in CTL immune response can induce not only Hopf bifurcation and double Hopf bifurcation, but also quasi-periodic orbits (torus) and coexistence of multiple stable periodic solutions. |
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