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Global properties of a delayed HIV infection model with CTL immune response. (English) Zbl 1245.92036

Summary: We study a delayed six-dimensional human immunodeficiency virus (HIV) model with Cytotoxic T Lymphocytes (CTLs) immune response. Our model describes the interaction of HIV with two target cells: \(CD4^{+}\) T cells and macrophages. We derive that the global asymptotic attractivity of the model is completely determined by the basic reproduction number \(R_{0}\) and the immune reproduction number \(R_0\) for the viral infection. By constructing Lyapunov functionals, we have shown that the infection-free equilibrium \(E_{0}\), the immune-free equilibrium \(E_{1}\) and the chronic-infection equilibrium \(E_{2}\) are globally asymptotically attractive when \(R_0\leq 1, R_0^*<R_0\) and \(R_0>R_0^*>1\), respectively.

MSC:

92C50 Medical applications (general)
92C60 Medical epidemiology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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