Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity

Wang, Tianlei; Hu, Zhixing; Liao, Fang; Ma, Wanbiao

doi:10.1016/j.matcom.2013.03.004

Cited by 77 publications

(65 citation statements)

References 23 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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“…However, as mentioned in [9], a general incidence rate may help us to gain the unification theory by the omission of unessential details. For more details about nonlinear incidence rates, we refer to see [10][11][12] and references cited in.…”

Section: Discrete Dynamics In Nature and Societymentioning

confidence: 99%

Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence

Geng

2017

Discrete Dynamics in Nature and Society

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In this paper, a discrete-time model has been proposed by applying nonstandard finite difference (NSFD) scheme to solve a delayed viral infection model with immune response and general nonlinear incidence. It is shown that the discrete model has equilibria which are exactly the same as those of the original continuous model. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria of the discrete model is fully determined by the basic reproduction number of the virus and immune response, R 0 and R 1 , with no restriction on the time step size, which implies that the NSFD scheme preserves the qualitative dynamics of the corresponding continuous model.

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“…We assume that the contacts between the viruses and uninfected target cells are given by an incidence function f (x, v). This form of incidence rate is general to encompass several forms of commonly used incidence rates such as bilinear incidence βxv [22], [28], saturated incidence βxv 1+ηv [25] and nonlinear incidence in the form f (x, v)v [27]. In [34] and [37], the viral infection models with general incidence rate f (x, v) have been studied, but without taking the humoral immune response into consideration.…”

Section: Model With General Incidence and Neutralization Ratesmentioning

confidence: 99%

Global Threshold Dynamics in Humoral Immunity Viral Infection Models Including an Eclipse Stage of Infected Cells

Ełaiw¹

2015

Journal of the Korea Society for Industrial and Applied Mathema

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ABSTRACT. In this paper, we propose and analyze three viral infection models with humoral immunity including an eclipse stage of infected cells. The incidence rate of infection is represented by bilinear incidence and saturated incidence in the first and second models, respectively, while it is given by a more general function in the third one. The neutralization rate of viruses is giv0en by bilinear form in the first two models, while it is given by a general function in the third one. For each model, we have derived two threshold parameters, the basic infection reproduction number which determines whether or not a chronic-infection can be established without humoral immunity and the humoral immune response activation number which determines whether or not a chronic-infection can be established with humoral immunity. By constructing suitable Lyapunov functions we have proven the global asymptotic stability of all equilibria of the models. For the third model, we have established a set of conditions on the threshold parameters and on the general functions which are sufficient for the global stability of the equilibria of the model. We have performed some numerical simulations for the third model with specific forms of the incidence and neutralization rates and have shown that the numerical results are consistent with the theoretical results.

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Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity

Cited by 77 publications

References 23 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

Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence

Global Threshold Dynamics in Humoral Immunity Viral Infection Models Including an Eclipse Stage of Infected Cells

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