A delayed HIV-1 model with virus waning term

Abstract

In this paper, we propose and analyze a delayed HIV-1 model with CTL immune response and virus waning. The two discrete delays stand for the time for infected cells to produce viruses after viral entry and for the time for CD8+ T cell immune response to emerge to control viral replication. We obtain the positiveness and boundedness of solutions and find the basic reproduction number R0. If R0 < 1, then the infection-free steady state is globally asymptotically stable and the infection is cleared from the T-cell population; whereas if R0 > 1, then the system is uniformly persistent and the viral concentration maintains at some constant level. The global dynamics when R0 > 1 is complicated. We establish the local stability of the infected steady state and show that Hopf bifurcation can occur. Both analytical and numerical results indicate that if, in the initial infection stage, the effect of delays on HIV-1 infection is ignored, then the risk of HIV-1 infection (if persists) will be underestimated. Moreover, the viral load differs from that without virus waning. These results highlight the important role of delays and virus waning on HIV-1 infection.

Stability of a general delay‐distributed virus dynamics model with multi‐staged infected progression and immune response

“…From Eq. (19), we obtain (19) and (H3), we have v 1 D~.x 1 / > 0, y i,1 D f i .x 1 / > 0, i D 1, : : : , n. It follows that a chronic-infection steady state with inactive humoral immunity S 1 D .x 1 , y 1,1 , : : : , y n,1 , v 1 , 0/ exists when…”

Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays

“…Over the recent years, several researchers have used mathematical models to explore the dynamics of various human pathogen infections. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Mathematical models and their analysis are helpful to enlighten the dynamical behavior of pathogens. Moreover, these models provide helpful suggestions for clinical treatment.…”

Stability of pathogen dynamics models with viral and cellular infections and immune impairment

“…[18,24,25,27,32,33,37,38,48]). The function φ(y, x) has been chosen in different forms such as: (i) constant, φ(y, x) = c 1 [31]; (ii) linear, φ(y, x) = ρy [1,23,44]; (iii) nonlinear φ(y, x) = c 2 yx (see e.g [27,30]). In these works, most pathogen infection models assume that the presence of the antigen can stimulate immunity and neglect the CTL immune impairment.…”