Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function

Yu, Yang; Ruan, Shigui; Xiao, Dongmei

doi:10.3934/mbe.2015.12.859

Cited by 44 publications

(22 citation statements)

References 26 publications

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“…The infection‐free steady state is globally asymptotically stable when the basic reproduction number is less than or equal to unity, and the infected steady state is globally asymptotically stable when the basic reproduction number is greater than one. Our analysis extends some existing results in the sense that the global stability was analyzed for a model with various types of target cell populations, and the general nonlinear rates, while some specific infection incidence assumptions, such as

β T V

F (T) G (V),

and

β T V / (1 + k_{1} T + k_{2} V)

, were used in . In addition, since our model was based on the HIV infection models which have convergent asymptotic dynamics in the long term, the result of this paper further shows that the incorporation of age‐infection does not change the global dynamics of within‐host virus infection model.…”

Section: Simulation and Conclusionsupporting

confidence: 59%

“…Most of the previous models were formulated based on the model in (see also in ). In recent years, the time delay between viral entry into a target cell and viral production was considered, by using a model with discrete and distributed delays , or an age‐structured model in the infected cell . The incorporation of an age structure (generally described by partial differential equations in theoretical models) allows us to have a good description of produced viral particles and of the infected cells mortality ().…”

Section: Introductionmentioning

confidence: 99%

“…However, debates exist for the infection incidence term, with some literatures arguing that the incidence rate should not be strictly linear in each variable over the entire range of virions

V (t)

and target cells

T (t)

and nonlinear contact rates are much more appropriate . For example, a virus infection rate with the Beddington–DeAngelis functional response

β T V / (1 + k_{1} T + k_{2} V)

was adopted in . Georgescu and Hsieh and Wang et al.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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β T V

F (T) G (V),

and

β T V / (1 + k_{1} T + k_{2} V)

Section: Simulation and Conclusionsupporting

confidence: 59%

Section: Introductionmentioning

confidence: 99%

“…However, debates exist for the infection incidence term, with some literatures arguing that the incidence rate should not be strictly linear in each variable over the entire range of virions

V (t)

and target cells

T (t)

and nonlinear contact rates are much more appropriate . For example, a virus infection rate with the Beddington–DeAngelis functional response

β T V / (1 + k_{1} T + k_{2} V)

was adopted in . Georgescu and Hsieh and Wang et al.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

2016

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“…Discussion. The global analysis of age-structured within-host virus model was studied by many authors such as [31] and [6]. To study the global stability of infection equilibrium, Browne and Pilyugin [6] assumed the "sector" condition, which does not hold for our model that incorporates proliferation of healthy cells.…”

mentioning

confidence: 99%

Hopf bifurcation of an age-structured virus infection model

Mohebbi¹,

Aminataei²,

Browne³

et al. 2018

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, we introduce and analyze a mathematical model of a viral infection with explicit age-since infection structure for infected cells. We extend previous age-structured within-host virus models by including logistic growth of target cells and allowing for absorption of multiple virus particles by infected cells. The persistence of the virus is shown to depend on the basic reproduction number R 0. In particular, when R 0 ≤ 1, the infection free equilibrium is globally asymptotically stable, and conversely if R 0 > 1, then the infection free equilibrium is unstable, the system is uniformly persistent and there exists a unique positive equilibrium. We show that our system undergoes a Hopf bifurcation through which the infection equilibrium loses the stability and periodic solutions appear.

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“… introduced a function to model the viral infection process of healthy target cells. The Beddington–DeAngelis function has been applied to a variety of disease models . Huang et al integrated the Beddington–DeAngelis functional response into a viral model and analyzed its global properties and investigated a delayed viral model with Beddington–DeAngelis functional response as well .…”

Section: Introductionmentioning

confidence: 99%

Dynamics of virus infection models with density‐dependent diffusion and Beddington–DeAngelis functional response

Wang

Zhang

et al. 2017

Math Methods in App Sciences

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In this work, we integrate both density-dependent diffusion process and Beddington-DeAngelis functional response into virus infection models to consider their combined effects on viral infection and its control. We perform global analysis by constructing Lyapunov functions and prove that the system is well posed. We investigated the viral dynamics for scenarios of single-strain and multi-strain viruses and find that, for the multi-strain model, if the basic reproduction number for all viral strains is greater than 1, then each strain persists in the host. Our investigation indicates that treating a patient using only a single type of therapy may cause competitive exclusion, which is disadvantageous to the patient's health. For patients infected with several viral strains, the combination of several therapies is a better choice.The classical Fickian diffusion equation assumes that random walkers in a system do not have interactions and has been used in a variety of models. However, individuals in real-world systems may interact, and as such, the diffusivity varies accordingly, known as the density-dependent diffusion [19]. Pao [20][21][22][23][24] performed a thorough study on a class of quasilinear parabolic and elliptic systems with mixed quasimonotone reaction functions and proved that the systems are well posed.Mathematical systems modeling the propagation of multiple virus strains have been considered in the literature to investigate the competitive exclusion and coexistence of pathogens. Bremerman and Thieme constructed an Susceptibles-Infectives-Recovers model with multiple viral strains. The authors investigated the model analytically and obtained its competitive exclusion [25]. Andreasen and Pugliese established a disease model and investigated the coexistence of two competing infectious diseases. The authors studied how the host density affects the viral transmission [26]. Andreasen et al. integrated a finite number of viral strains into a disease model to reveal the immunity structure of the host population [27]. Feng et al. established an SIR model with two viral strains to consider the spread of a vector-borne disease [28]. Martcheva and Pilyugin established a multi-disease model and performed investigations on its bistability and bifurcation [29]. Castillo-Chavez et al. designed an susceptible-infective-susceptible sexually transmitted disease model to describe the transmission of two competing viral strains [30]. Iggidr et al. established an age-structured Malaria intra-host model with n viral strains and analyzed its global property [31]. Leenheer and Pilyugin studied the effects of viral mutation on the behaviors of a within-host multi-virus model [32]. The authors used a Lyapunov function to prove the global stability of the model's steady state.Dai and Zou established an age-structured within-host model and studied its global stability to investigate the interplay between two viral strains with viral mutations [33].The diffusion of virions is responsible for the short-range infections. Such vira...

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Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function

Cited by 44 publications

References 26 publications

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

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

Hopf bifurcation of an age-structured virus infection model

Dynamics of virus infection models with density‐dependent diffusion and Beddington–DeAngelis functional response

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