Stability and Hopf bifurcation of an HIV infection model with two time delays

Yu Yang; Gang Huang; Yueping Dong; Yu Yang; Gang Huang; Yueping Dong

doi:10.3934/mbe.2023089

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 1938-1959. doi: 10.3934/mbe.2023089

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Stability and Hopf bifurcation of an HIV infection model with two time delays

1.
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
2.
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Academic Editor: Xiang-Sheng Wang

Received: 04 September 2022 Revised: 25 October 2022 Accepted: 30 October 2022 Published: 09 November 2022

This work focuses on an HIV infection model with intracellular delay and immune response delay, in which the former delay refers to the time it takes for healthy cells to become infectious after infection, and the latter delay refers to the time when immune cells are activated and induced by infected cells. By investigating the properties of the associated characteristic equation, we derive sufficient criteria for the asymptotic stability of the equilibria and the existence of Hopf bifurcation to the delayed model. Based on normal form theory and center manifold theorem, the stability and the direction of the Hopf bifurcating periodic solutions are studied. The results reveal that the intracellular delay cannot affect the stability of the immunity-present equilibrium, but the immune response delay can destabilize the stable immunity-present equilibrium through the Hopf bifurcation. Numerical simulations are provided to support the theoretical results.
- HIV infection model,
- intracellular delay,
- immune response delay,
- stability analysis,
- Hopf bifurcation
Citation: Yu Yang, Gang Huang, Yueping Dong. Stability and Hopf bifurcation of an HIV infection model with two time delays[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 1938-1959. doi: 10.3934/mbe.2023089

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Abstract

This work focuses on an HIV infection model with intracellular delay and immune response delay, in which the former delay refers to the time it takes for healthy cells to become infectious after infection, and the latter delay refers to the time when immune cells are activated and induced by infected cells. By investigating the properties of the associated characteristic equation, we derive sufficient criteria for the asymptotic stability of the equilibria and the existence of Hopf bifurcation to the delayed model. Based on normal form theory and center manifold theorem, the stability and the direction of the Hopf bifurcating periodic solutions are studied. The results reveal that the intracellular delay cannot affect the stability of the immunity-present equilibrium, but the immune response delay can destabilize the stable immunity-present equilibrium through the Hopf bifurcation. Numerical simulations are provided to support the theoretical results.

References

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