Global dynamics of a diffusive and delayed viral infection model with cellular infection and nonlinear infection rate

Xu, Jin; Geng, Yan; Hou, Jiangyong

doi:10.1016/j.camwa.2016.12.032

Cited by 10 publications

(12 citation statements)

References 33 publications

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“…As a result, the main purpose of the present paper is to explore the dynamics of the diffusive viral model (1.4). The similar research can be found in [23,25].…”

Section: Introductionsupporting

confidence: 67%

Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response

Zhuang¹

2017

J. Nonlinear Sci. Appl.

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In this paper, a four-dimensional system of viral model with cytotoxic lymphocyte (CTL) immune response is investigated. This model is a reaction-diffusion system with Beddington-DeAngelis incidence rate and free diffusion in a bounded domain. With the help of comparison principle and Lyapunov function method, the well-posedness of solutions and sufficient conditions for global stability of nonnegative equilibria are established. It can be found that free diffusion has no influence on the global stability of the system with homogeneous Neumann boundary conditions.

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“…As a result, the main purpose of the present paper is to explore the dynamics of the diffusive viral model (1.4). The similar research can be found in [23,25].…”

Section: Introductionsupporting

confidence: 67%

Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response

Zhuang¹

2017

J. Nonlinear Sci. Appl.

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“…where = max{ 1 , 2 } and 2,3,4,5). In this paper, we will present an affirmative answer that the discrete model (6) which derived by utilizing Mickens' method can efficiently preserve the global properties to the original continuous model (2).…”

Section: Discrete Dynamics In Nature and Societymentioning

confidence: 84%

“…Epidemiologically, condition (3) indicates that (i) the disease can not spread if there is no infection; (ii) the incidences ( ) become faster as the densities of the virions increase; (iii) the per capita infection rates by virions will slow down due to certain inhibition effect since (4) implies that ( ( )/ ) ≤ 0.…”

Section: Discrete Dynamics In Nature and Societymentioning

confidence: 99%

“…The classical model for within host virus dynamics is a system which includes three ordinary differential equations [1,2]. However, to take some features into consideration of a real system, like time delay, age structure, and so on, many literatures have been proposed and studied (see [3][4][5][6][7][8] and references therein). For example, Manna [8] …”

Section: Introductionmentioning

confidence: 99%

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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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“…In 2017, Xu et al [30] proposed a PDE model with two discrete delays, cell-to-cell transmission and CTL immune response. They considered the spatial diffusion only in virus.…”

Section: Global Stabilitymentioning

confidence: 99%

Spatiotemporal Dynamics of a Generalized Viral Infection Model with Distributed Delays and CTL Immune Response

Hattaf

2019

Computation

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In this paper, we propose and investigate a diffusive viral infection model with distributed delays and cytotoxic T lymphocyte (CTL) immune response. Also, both routes of infection that are virus-to-cell infection and cell-to-cell transmission are modeled by two general nonlinear incidence functions. The well-posedness of the proposed model is also proved by establishing the global existence, uniqueness, nonnegativity and boundedness of solutions. Moreover, the threshold parameters and the global asymptotic stability of equilibria are obtained. Furthermore, diffusive and delayed virus dynamics models presented in many previous studies are improved and generalized.

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Global dynamics of a diffusive and delayed viral infection model with cellular infection and nonlinear infection rate

Cited by 10 publications

References 33 publications

Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response

Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response

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

Spatiotemporal Dynamics of a Generalized Viral Infection Model with Distributed Delays and CTL Immune Response

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