Stability of a general CTL-mediated immunity HIV infection model with silent infected cell-to-cell spread

Advances in Difference Equations

article

Elaiw, A. M.¹  AlShamrani, N. H.¹ 

[1] Department of Mathematics, Faculty of Science, King Abdulaziz University;Department of Mathematics, Faculty of Science, Al-Azhar University;Department of Mathematics, Faculty of Science, University of Jeddah

关键词: HIV infection;    Cell-to-cell spread;    Global stability;    Silent infected cells;    CTL-mediated immune response;    Lyapunov function;   

DOI  :  10.1186/s13662-020-02818-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY