Abstract
This paper proposes and investigates an HIV dynamics model with adaptive immunity. The model describes the interactions between five compartments: healthy CD4+T cells, silent infected cells, active infected cells, free HIV particles, and cytotoxic T lymphocytes and antibodies. The model incorporates two methods of transmission: virus-to-cell and cell-to-cell (CTC). The healthy cells can be infected when they come into contact with free HIV particles or silent infected cells or active infected cells. We established that the model is well-posed by establishing the nonnegativity and boundedness of the solutions. The model has admitted five equilibria, and their existence is governed by five threshold parameters. We prove the global asymptotic stability of the equilibria by constructing Lyapunov functions. We have illustrated the theoretical results by numerical simulations. We have shown that the inclusion of CTC transmission decreases the concentration of healthy cells and increases the concentration of free HIV particles.
Highlights
Human immunodeficiency virus (HIV) infects the human body and causes acquired immunodeficiency syndrome (AIDS), which is one of the dangerous human diseases
We showed that the model has five possible equilibria, and their existence is determined by five threshold parameters
The global asymptotic stability of all equilibria was investigated by constructing Lyapunov functionals and utilizing LaSalle’s invariance principle
Summary
Human immunodeficiency virus (HIV) infects the human body and causes acquired immunodeficiency syndrome (AIDS), which is one of the dangerous human diseases. ΠP, ζT, where W = W(t), M = M(t), N = N(t), P = P(t), and T = T(t) are the concentrations of healthy CD4+T cells, active HIV-infected cells, free HIV particles, HIV-specific CTLs, and HIV-specific antibodies at time t, respectively. The term μPM is the killing rate of active HIV-infected cells due to their specific CTL-mediated immunity. We first formulate an HIV dynamics model with both CTL-mediated and antibody immune responses. Both VTC and CTC transmissions have been considered. The CTC transmission is due to the contact of healthy CD4+T cells with silent or active HIV-infected cells.
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