Stability and Hopf bifurcation for a virus infection model with delayed humoral immunity response

Wang, Tianlei; Hu, Zhixing; Liao, Fang

doi:10.1016/j.jmaa.2013.09.035

Cited by 71 publications

(44 citation statements)

References 20 publications

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“…In the virus dynamics literature, several mathematical models have incorporated CTL immune response 2-5 and humoral immune response. [6][7][8][9][10][11] Intracellular time delay discrete or distributed has also been considered in the mathematical models of virus dynamics in several works (see e.g., Refs. 13 and 12-18.…”

Section: Introductionmentioning

confidence: 99%

“…It is observed that, no HIV infection model with this type of infected-to-target infection has considered the effect of immune response. Humoral immunity has been incorporated into virus dynamics models in several works, [6][7][8][9][10][11] however, in these papers, only virus-to-cell transmission has been considered. Therefore, reasonable mathematical models for HIV-1 with virus-to-target and infected-to-target infections should take humoral immunity into consideration.…”

Section: Introductionmentioning

confidence: 99%

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Effect of humoral immunity on HIV-1 dynamics with virus-to-target and infected-to-target infections

2016

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We consider an HIV-1 dynamics model by incorporating (i) two routes of infection via, respectively, binding of a virus to a receptor on the surface of a target cell to start genetic reactions (virus-to-target infection), and the direct transmission from infected cells to uninfected cells through the concept of virological synapse in vivo (infected-to-target infection); (ii) two types of distributed-time delays to describe the time between the virus or infected cell contacts an uninfected CD4+ T cell and the emission of new active viruses; (iii) humoral immune response, where the HIV-1 particles are attacked by the antibodies that are produced from the B lymphocytes. The existence and stability of all steady states are completely established by two bifurcation parameters, R0 (the basic reproduction number) and R1 (the viral reproduction number at the chronic-infection steady state without humoral immune response). By constructing Lyapunov functionals and using LaSalle’s invariance principle, we have proven that, if R0≤1, then the infection-free steady state is globally asymptotically stable, if R1≤1<R0, then the chronic-infection steady state without humoral immune response is globally asymptotically stable, and if R1>1, then the chronic-infection steady state with humoral immune response is globally asymptotically stable. We have performed numerical simulations to confirm our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of humoral immunity on HIV-1 dynamics with virus-to-target and infected-to-target infections

2016

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“…In addition, there are some models considered only one type of adaptive immunity. For example, works with only the CTL response are presented in [5][6][7][8][9] and others with only antibody response are described in [10][11][12].…”

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confidence: 99%

Dynamics of a generalized viral infection model with adaptive immune response

Hattaf

Khabouze

Yousfi

2014

Int. J. Dynam. Control

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A mathematical model for viral infection is formulated by five nonlinear differential equations to describe the interactions between virus, host cells, and the adaptive immune response represented by cytotoxic T lymphocytes (CTL) cells and the antibodies. The infection transmission process is modeled by a general incidence function which covers several forms existing in models that studied viral infections such as HIV and HBV infections. Based on the direct Lyapunov method, the global stability of the equilibria is investigated. Furthermore, under certain hypotheses on the incidence function it is proved that the dynamical behavior of the model is fully characterized by the reproduction numbers for viral infection R 0 , for CTL immune response R z 1 , for antibody immune response R w 1 , for CTL immune competition R z 2 and for antibody immune competition R w 3 .

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“…It is well known that the time delay occurs naturally in daily life and makes ecological systems have more complex dynamic behaviors. Therefore, ecological systems with time delay have been investigated in recent years (discrete delays [8][9][10][11][12][13][14][15], neutral delays [16,17] and impulsive delay [18]). Taking the time delay as a parameter, the stability of the equilibrium may be changed and periodic solutions may occur as the time delay varies.…”

Section: Introductionmentioning

confidence: 99%

Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay

Yao

Xiang

et al. 2018

Adv Differ Equ

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In this paper, dynamic behaviors of a turbidostat model with Tissiet functional response, linear variable yield and time delay are investigated. The existence and boundedness of solutions, the local asymptotic stability of its equilibria and the phenomenon of Hopf bifurcation for this system are considered. Using the Liapunov-LaSalle invariance principle, we show that the washout equilibrium is global asymptotic stability for any time delay. Furthermore, based on some knowledge of limit set, we show the necessary and sufficient conditions of permanent of the turbidostat model. Finally, numerical simulations are offered to support our results.

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Stability and Hopf bifurcation for a virus infection model with delayed humoral immunity response

Cited by 71 publications

References 20 publications

Effect of humoral immunity on HIV-1 dynamics with virus-to-target and infected-to-target infections

Effect of humoral immunity on HIV-1 dynamics with virus-to-target and infected-to-target infections

Dynamics of a generalized viral infection model with adaptive immune response

Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay

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