A class of delayed virus dynamics models with multiple target cells

Wang, Xia; Chen, Yuefen; Liu, Shengqiang; Song, Xinyu

doi:10.1007/s40314-013-0004-z

Cited by 8 publications

(7 citation statements)

References 36 publications

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“…In this case, with the consideration of different types of target cells, models with more compartments can be proposed, such as those in . Recently, the global dynamics of the steady states of HIV models with multiple target cells was investigated in .…”

Section: Introductionmentioning

confidence: 99%

Age‐Structured Within‐Host HIV Dynamics with Multiple Target Cells

2016

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Human immunodeficiency virus (HIV) can infect various types of cell populations such as CD4 + T cells and macrophages. The heterogeneity of these target cells implies different birth, death, infection rates, and so on. To investigate the within-host dynamics of HIV which can infect n different types of target cells, a theoretical model with infection-age structure for each type of target cells and a general nonlinear incidence rate is proposed in this manuscript. The model, in the form of a hyperbolic system of partial differential equations (PDE) for infected target cells coupled with several ordinary differential equations, is shown to be biologically reasonable with the establishment of existence, positivity, and boundedness of solutions. Although the PDE form poses novel challenges to theoretical investigation, rigorous analysis is performed to show the uniform persistence of the virus when the basic reproduction number is greater than one. Furthermore, by constructing suitable Lyapunov functionals, we show that the infection-free steady state is globally asymptotically stable when the basic reproduction number is less than unity, while the positive steady state is globally asymptotically stable when the basic reproduction number is greater than one.

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Section: Introductionmentioning

confidence: 99%

Age‐Structured Within‐Host HIV Dynamics with Multiple Target Cells

2016

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“…The viral infection models describing the interaction of the virus with more than one class of target cells can be found in the literature, such as [3,4,6,18,21] and references cited therein. In these models, HIV attack two classes of target cells, CD4 + T cells and macrophages.…”

Section: Introductionmentioning

confidence: 99%

“…Our global stability result for the infection equilibrium is new for in-host models with finite distributed intracellular delays. Our proof utilizes the Lyapunov method motivated by the work in [3,9,10,12,14,15,16,19,20,21,22,23,24,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Constructing Lyapunov functionals for a delayed viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate

Wang¹,

Lang²,

Li³

2016

J. Nonlinear Sci. Appl.

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For a viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate and distributed delays, we analyze the global asymptotic behavior of its solutions. In this model, the rate of contact between viruses and uninfected target cells and state-dependent removal rate of infected cells depend on general nonlinear functions. The basic reproduction number for the model is discussed. Under certain assumptions, it is shown that if 0 ≤ 1, then the infection-free equilibrium P 0 is globally stable and the viruses are cleared; If 0 > 1, then there is a unique infection equilibrium, which is globally stable implying the infection becomes chronic. The global stability results are achieved by appealing to the direct Lyapunov method.

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“…In [2,25], an HIV model was analyzed in which two target cells, CD4 + T cells and macrophages are subjected to infection by virus. Particular, some of recent studies [5,7,28] with two target cells and discrete and distributed delays was analyzed. In [6,8], a class of viral infection model was studied in the case where multiple classes of target cells can be attacked by virus.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis for delayed viral infection model with multitarget cells and general incidence rate

2015

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In this paper, the sharp threshold properties of a (2n + 1)-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected target cells, n classes of infected cells and nonlinear incidence rate h (x, v). Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model. Int. J. Biomath. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/19/15. For personal use only. Stability analysis for delayed viral infection model39], which lead mathematical models to delay differential equations. It is of interest from both mathematical and biological viewpoints to investigate whether Hopf bifurcations in in-host models are the result of target-cell dynamics, intracellular delays, or a combination of both. The result that intracellular delays will lead to period oscillations in in-host models only with the right kind of target-cell dynamics has been shown in Li et al. [17].Motivated by the studies of [12-15, 17, 19, 21], the main purpose of this paper is to give the conditions to ensure the permanence and complete global analysis of the 2n + 1-dimensional viral infection model. The model studied in this paper (compared to model (1.1)) include the following extensions:

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A class of delayed virus dynamics models with multiple target cells

Cited by 8 publications

References 36 publications

Age‐Structured Within‐Host HIV Dynamics with Multiple Target Cells

Age‐Structured Within‐Host HIV Dynamics with Multiple Target Cells

Constructing Lyapunov functionals for a delayed viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate

Stability analysis for delayed viral infection model with multitarget cells and general incidence rate

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