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Modelling HIV dynamics with cell-to-cell transmission and CTL response
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  • Zirui Zhu,
  • Ranchao Wu,
  • Yu Yang,
  • Yancong Xu
Zirui Zhu
Hangzhou Normal University

Corresponding Author:[email protected]

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Ranchao Wu
Anhui University
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Yu Yang
Shanghai Lixin University of Accounting and Finance
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Yancong Xu
Hangzhou Normal University
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In most HIV models, the emergence of backward bifurcation means that the control for basic reproduction number less than one is no longer effective for HIV treatment. In this paper, we study an HIV model with CTL response and cell-to-cell transmission by using the dynamical approach. The local and global stability of equilibria is investigated, the relations of subcritical Hopf bifurcation and supercritical bifurcation points are revealed, especially, the so-called new type bifurcation is also found with two Hopf bifurcation curves meeting at the same Bogdanov-Takens bifurcation point. Forward and backward bifurcation, Hopf bifurcation, saddle-node bifurcation, Bogdanov-Takens bifurcation are investigated analytically and numerically. Two limit cycles are also found numerically, which indicates that the complex behavior of HIV dynamics. Interestingly, the role of cell-to-cell interaction is fully uncovered, it may cause the oscillations to disappear and keep the so-called new type bifurcation persist. Finally, some conclusions and discussions are also given.
17 Aug 2021Submitted to Mathematical Methods in the Applied Sciences
18 Aug 2021Submission Checks Completed
18 Aug 2021Assigned to Editor
24 Aug 2021Reviewer(s) Assigned
14 Jan 2022Review(s) Completed, Editorial Evaluation Pending
15 Jan 2022Editorial Decision: Revise Major
07 Feb 20221st Revision Received
08 Feb 2022Assigned to Editor
08 Feb 2022Submission Checks Completed
09 Feb 2022Reviewer(s) Assigned
26 Mar 2022Review(s) Completed, Editorial Evaluation Pending
06 Jun 2022Editorial Decision: Revise Minor
13 Jun 20222nd Revision Received
14 Jun 2022Submission Checks Completed
14 Jun 2022Assigned to Editor
14 Jun 2022Reviewer(s) Assigned
06 Aug 2022Review(s) Completed, Editorial Evaluation Pending
04 Nov 2022Editorial Decision: Accept
Apr 2023Published in Mathematical Methods in the Applied Sciences volume 46 issue 6 on pages 6506-6528. 10.1002/mma.8921