Global Dynamics of a Delayed HIV‐1 Infection Model with CTL Immune Response

Abstract

A delayed HIV-1 infection model with CTL immune response is investigated. By using suitable Lyapunov functionals, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection is less than or equal to unity; if the basic reproduction ratio for CTL immune response is less than or equal to unity and the basic reproduction ratio for viral infection is greater than unity, the CTL-inactivated infection equilibrium is globally asymptotically stable; if the basic reproduction ratio for CTL immune response is greater than unity, the CTL-activated infection equilibrium is globally asymptotically stable.

Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model

“…One interpretation for this approximation is that it would be valid when the time delay is small. Similar models have been studied by other authors, see for example Wang et al [39], Li et al [22] and Yang et al [43]. A similar idea is also used in other contexts by McCluskey [26], Bachar and Dorfmayr [1] and many other authors, see also our previous discussion.…”

“…A model which takes into account death of contacted cells during the incubation period is used by Culshaw et al [7] and Zhu and Zou [44]. However these deaths are ignored as an approximation by other authors (Shi et al [35], Li and Ma [21], McCluskey [26] and Li et al [22]). Because in our model the contacted cells remain in the susceptible class rather than progressing to the incubating class, as well as deaths we must also take account of those contacted T cells which exit the susceptible class during the time interval [t − τ, t) because of also previously being contacted in the time interval [t − 2τ, t − τ ), as described in equations (1.10).…”

Spatiotemporal Dynamics of a Generalized Viral Infection Model with Distributed Delays and CTL Immune Response

“…Since R 0 and R Z 1 have no relation to the diffusion coefficients d T , d I , d V and d Z , we conclude that the diffusion of cells and virus has no effect on the global stability of the three steady states of our PDE model with Neumann homogeneous boundary conditions. On the other hand, we have extended the models with ODEs [1,4,5], with DDEs [6][7][8][9] and with PDEs [17][18][19]. Moreover, the more recent works presented in [30,31] are improved and generalized.…”

“…In reality, there are two routes of infection and also time delays in cell infection and virus production. Motivated by these biological reasons, Li et al [6] proposed a mathematical model formulated by delay differential equations (DDEs) to describe the global dynamics of HIV infection with CTL immune response. This delayed model is an extension of [1] that considers Holling type-II functional response and two kinds of discrete delays, one in cell infection and the other in virus production.…”

“…Furthermore, a recent work presented in [9] studied the dynamical behavior of a viral infection model with two types of distributed time delays, CTL immune response and saturated incidence rates for both routes of infection. In this paper, we generalize all the ODE and DDE models presented in [1,[4][5][6][7][8][9] by proposing the following nonlinear system:…”