Global behavior of delay differential equations model of HIV infection with apoptosis

Abstract

In this paper, a class of delay differential equations model of HIV infection dynamics with nonlinear transmissions and apoptosis induced by infected cells is proposed, and then the global properties of the model are considered. It shows that the infection-free equilibrium of the model is globally asymptotically stable if the basic reproduction number R 0 < 1, and globally attractive if R 0 = 1. The positive equilibrium of the model is locally asymptotically stable if R 0 > 1. Furthermore, it also shows that the model is permanent, and some explicit expressions for the eventual lower bounds of positive solutions of the model are given.

Dynamics analysis of a delayed virus model with two different transmission methods and treatments

“…Using mathematical models to help discover the mechanism of viral transmission to predict the development of infectious diseases has become the mainstream method for controlling and preventing infectious diseases [9][10][11][12]. Therefore, for over a century, lots of mathematical models have been established to explain the evolution of the free virus in a body, and mathematical analysis was implemented to explore the threshold associated with eradication and persistence of the virus; for example, [13][14][15][16] studied the global dynamic behavior of HIV models, [17][18][19][20][21][22][23][24] analysed the global dynamics of HBV models [25][26][27][28]. A general class of models describing the process of virus invading the target cells and release of the virus due to the infected cell apoptosis has been established and analyzed by Perelson et al [29,30] and Nelson et al [31] as follows:…”

Threshold dynamics and threshold analysis of HIV infection model with treatment

“…Recently, Guo and Ma [6] first proposed a class of delay differential equations model of HIV infection dynamics with the intracellular delay, apoptosis induced by infected cells, and a general incidence function, and then analyzed the global properties of the model.…”

Modeling Cell‐to‐Cell Spread of HIV‐1 with Nonlocal Infections

“…Many diseases are caused by a virus, for example, human immunodeficiency virus (HIV) can destroy the immune cells, reduce human immunity, and ultimately lead to AIDS. A lot of mathematical models have been built to explain the virus infection process from different views [12][13][14][15]. In recent years, the virus infection dynamical models incorporating spatial dispersion [16,17] have received widely attentions.…”