Speaker
Description
We investigate a class of autonomous fractional-order nonlinear dynamical systems motivated by an in-host HIV infection model incorporating three structural mechanisms: logistic proliferation of healthy target cells, two transmission pathways--virus-to-cell infection and cell-to-cell transmission through virological synapses~\cite{kai2010analysis,lai2014model,chen2016stability,chen2019within}--and Caputo fractional-order derivatives accounting for memory effects. A threshold parameter, formulated as the basic reproduction number $R_0$, is derived and shown to govern the global dynamics. Specifically, the infection-free equilibrium is globally asymptotically stable when $R_0<1$, whereas uniform persistence is established when $R_0>1$. The local stability of the endemic equilibrium is further examined, and parameter regimes associated with a transition from steady-state convergence to oscillatory dynamics are identified. Due to intrinsic properties of autonomous fractional-order systems, exact periodic solutions and classical Hopf bifurcations are not expected. Instead, the observed oscillatory behavior corresponds to Hopf-type instability manifested through long-lasting transient or quasi-periodic dynamics. Although the fractional order does not modify the threshold structure determined by $R_0$, it significantly influences convergence rates and qualitative asymptotic behavior, highlighting fundamental dynamical distinctions between integer-order and fractional-order systems.
Bibliography
@incollection{kai2010analysis,
title={The analysis of fractional differential equations: An application-oriented exposition using differential operators of {Caputo} type},
author={Kai, Diethelm},
booktitle={Lecture Notes in Mathematics},
year={2010},
publisher={Springer}
}
@article{lai2014model,
title={Modeling {HIV}-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission},
author={Lai, Xiulan and Zou, Xingfu},
journal={SIAM Journal on Applied Mathematics},
volume={74},
number={3},
pages={898--917},
year={2014},
publisher={SIAM}
}
@article{chen2016stability,
title={Stability analysis in delayed within-host viral dynamics with both viral and cellular infections},
author={Chen, Shyan-Shiou and Cheng, Chang-Yuan and Takeuchi, Yasuhiro},
journal={Journal of Mathematical Analysis and Applications},
volume={442},
number={2},
pages={642--672},
year={2016},
publisher={Elsevier}
}
@article{chen2019within,
title={Within-host viral dynamics in a multi-compartmental environment},
author={Chen, Shyan-Shiou and Cheng, Chang-Yuan and Rong, Libin},
journal={Bulletin of Mathematical Biology},
volume={81},
pages={4271--4308},
year={2019},
publisher={Springer}
}
