Abstract
This paper proposes and analyzes a CTL-mediated HIV infection model. The model describes the interaction between healthy CD4+T cells, silent infected cells, active infected cells, free HIV particles, and cytotoxic T lymphocytes (CTLs). The healthy CD4+T cells can be infected when contacted by one of the following: (i) free HIV particles, (ii) silent infected cells, and (iii) active infected cells. The incidence rates of the healthy CD4+T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the incidence between the silent infected cells and healthy CD4+T cells. We first show that the model is well posed. The proposed model has three equilibria and their existence is governed by derived two threshold parameters: the basic HIV reproduction number Re _{0} and the HIV-specific CTL-mediated immunity reproduction number Re _{1}. Under a set of conditions on the general functions and the parameters Re _{0} and Re _{1}, we have proven the global asymptotic stability of all equilibria by using Lyapunov method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of cell-to-cell (CTC) transmission on the dynamical behavior of the system. We have shown that inclusion of CTC transmission decreases the concentration of healthy CD4+T cells and increases the concentrations of infected cells and free HIV particles.
Highlights
Acquired immunodeficiency syndrome (AIDS) is one of the fatal human diseases which is caused by human immunodeficiency virus (HIV)
The incidence rates between the healthy CD4+T cells and free HIV particles, silent infected cells, and active infected cells were given by general functions
We showed that the model has three possible equilibria: the infection-free equilibrium Ð0, the chronic HIV infection equilibrium with inactive cytotoxic T lymphocytes (CTLs)-mediated immune response Ð1, and the chronic HIV infection equilibrium with active CTL-mediated immune response Ð2
Summary
Acquired immunodeficiency syndrome (AIDS) is one of the fatal human diseases which is caused by human immunodeficiency virus (HIV). Silent HIV-infected cells have been included in the virus dynamics models with both VTC and CTC transmissions in [35,36,37,38,39]. We first formulate an HIV infection model with CTL-mediated immune response and both VTC and CTC transmissions.
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