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Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays

  • Hui Miao EMAIL logo and Meiyan Jiao
Published/Copyright: March 4, 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 2

Abstract

In this paper, the dynamical behaviors of a multiple delayed HIV-1 infection model which describes the interactions of humoral, cytotoxic T lymphocyte (CTL) immune responses, and two modes of transmission that are the classical virus-to-cell infection and the direct cell-to-cell transmission are investigated. The model incorporates three delays, including the delays of cell infection, virus production and activation of immune response. We first prove the well-posedness of the model, and calculate the biological existence of equilibria and the reproduction numbers, which contain virus infection, humoral immune response, CTL immune response, CTL immune competition, and humoral immune competition. Further, the threshold conditions for the local and global stability of the equilibria for infection-free, immune-free, antibody response, CTL response, and interior are established by utilizing linearization method and the Lyapunov functionals. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is investigated by using the bifurcation theory. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics.

Keywords: CTL immunity; HIV-1 infection; Hopf bifurcation; humoral immunity; stability
Corresponding author: Hui Miao, School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, P.R. China, E-mail:

Funding source: the National Natural Science Foundation of China

Award Identifier / Grant number: 11901363

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This work was supported by the National Natural Science Foundation of China (Grant nos. 11901363 and 11771373), Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (Grant no. 2021L279), and the Youth Research Fund for the Shanxi basic research project (Grant no. 2015021025).

  3. Conflict of interest statement: The authors declare that there is no conflict of interests regarding the publication of this paper.

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Received: 2021-06-27
Revised: 2021-12-05
Accepted: 2022-02-03
Published Online: 2022-03-04

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
  4. Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays
  5. Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model
  6. On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations
  7. On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale
  8. A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces
  9. Solitary waves of the RLW equation via least squares method
  10. Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber
  11. Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces
  12. Modified inertial subgradient extragradient method for equilibrium problems
  13. Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications
  14. Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
  15. Investigation of nonlinear fractional delay differential equation via singular fractional operator
  16. Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions
  17. The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions
  18. Stability and ψ-algebraic decay of the solution to ψ-fractional differential system
  19. Some new characterizations of a space curve due to a modified frame N ⃗ , C ⃗ , W ⃗ in Euclidean 3-space
  20. Numerical simulation of particulate matter propagation in an indoor environment with various types of heating
  21. Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces
  22. Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics
  23. Contrasting effects of prey refuge on biodiversity of species
https://doi.org/10.1515/ijnsns-2021-0263
Keywords for this article
CTL immunity; HIV-1 infection; Hopf bifurcation; humoral immunity; stability

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
  4. Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays
  5. Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model
  6. On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations
  7. On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale
  8. A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces
  9. Solitary waves of the RLW equation via least squares method
  10. Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber
  11. Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces
  12. Modified inertial subgradient extragradient method for equilibrium problems
  13. Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications
  14. Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
  15. Investigation of nonlinear fractional delay differential equation via singular fractional operator
  16. Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions
  17. The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions
  18. Stability and ψ-algebraic decay of the solution to ψ-fractional differential system
  19. Some new characterizations of a space curve due to a modified frame N ⃗ , C ⃗ , W ⃗ in Euclidean 3-space
  20. Numerical simulation of particulate matter propagation in an indoor environment with various types of heating
  21. Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces
  22. Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics
  23. Contrasting effects of prey refuge on biodiversity of species
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