Global stability for a class of HIV infection models with cure of infected cells in eclipse stage and CTL immune response

A Fractional Order Model for Viral Infection with Cure of Infected Cells and Humoral Immunity

“…, where 0 , 1 , 2 , 3 ≥ 0 are the saturation factors measuring the psychological or inhibitory effect and > 0 is the infection rate. In addition, this functional response generalizes many common types existing in the literature such as the specific functional response proposed by Hattaf et al in [37] and used in [2,31] when 0 = 1; the Crowley-Martin functional response introduced in [38] and used in [39] when 0 = 1 and 3 = 1 2 ; and the Beddington-DeAngelis functional response proposed in [40,41] and used in [3,4,10] when 0 = 1 and 3 = 0. Also, the Hattaf-Yousfi functional response is reduced to the saturated incidence rate used in [9] when 0 = 1 and 1 = 3 = 0 and the standard incidence function used in [27] when 0 = 3 = 0 and 1 = 2 = 1, and it was simplified to the bilinear incidence rate used in [5,6] when 0 = 1 and…”

“…Therefore, many mathematical models have been developed to incorporate the role of immune response in viral infections. Some of these models considered the cellular immune response mediated by cytotoxic T lymphocytes (CTL) cells that attack and kill the infected cells [1][2][3][4][5] and the others considered the humoral immune response based on the antibodies which are produced by the B-cells and are programmed to neutralize the viruses [6][7][8][9][10][11]. However, all these models have been formulated by using ordinary differential equations (ODEs) in which the memory effect is neglected while the immune response involves memory [12,13].…”

Stability and bifurcation analysis of an HIV-1 infection model with a general incidence and CTL immune response

“…With the Lyapunov direct method, established are conditions on the global stability of equilibria in terms of the basic reproduction number and the immune response reproduction number. Later on, Maziane et al [20] considered a variation of (2) by replacing βxv 1+mx+nv with βxv 1+α 1 x+α 2 v+α 3 xv and similar results were derived. Motivated by the above discussion, in this paper, we investigate the following HIV-1 infection model with eclipse phase and CTL immune response,…”

Global stability of a fractional order HIV infection model with cure of infected cells in eclipse stage

“…In the same years, Boukhouima et al [4] generalized all the above models by modeling the infection transmission process by Hattaf's incidence rate [5]. This incidence rate was used by many authors [6][7][8][9] and it covers many common types existing in the literature, such as the bilinear incidence function called also the mass action, the saturation incidence rate, the Beddington-DeAnglis functional response [10,11] and the Crowley-Martin functional response [12]. In the above fractional-order models [1][2][3][4], infected cells are assumed to produce new virions immediately after target cells are infected by a free virus.…”