1. Stability and Hopf bifurcation of a cytokine-enhanced HIV infection model with antibody immune response delay.
- Author
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Ye, Zhijian, Zhou, Yinggao, Zheng, Zhoushun, and Chen, Chong
- Abstract
In this paper, the dynamical behaviors of a new cytokine-enhanced HIV infection model with intracellular delay τ1, virus replication delay τ2 and immune response delay τ3 are investigated. The positivity and boundedness of all solutions for the model with non-negative initial values have been proved. Moreover, two important biological parameters, called the virus reproductive number R0 and the antibody immune reproductive number R1 are established. By constructing suitable Lyapunov functionals and using LaSalle’s invariance principle, the global dynamics of the equilibria is completely determined by R0 and R1. On the one hand, the results show that intracellular delay τ1, viral replication delay τ2 and immune response delay τ3 have no effect on the stability of E0, E1, and if τ1 ≥ 0, τ2 ≥ 0, τ3 = 0, the endemic equilibrium with the presence of antibody response E2 is globally asymptotically stable. On the other hand, when τ1 ≥ 0, τ2 ≥ 0, τ3 > 0, numerical analysis confirms the theorems and suggests that time delay play a positive role in virus infection, with the increase of τ3, the dynamic behavior of the equilibrium E2 will change as follows: locally asymptotically stable → unstable; Hopf bifurcation appears. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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