Global stability of one and two discrete delay models for chronic hepatitis B infection with HBV DNA-containing capsids

Manna, Kalyan; Chakrabarty, Siddhartha P.

doi:10.1007/s40314-015-0242-3

Cited by 42 publications

(30 citation statements)

References 26 publications

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“…We first study the global dynamics of the continuous system (2) in Section 2. In Section 3, we investigate the global dynamics of discrete system (6). A brief conclusion ends the paper.…”

Section: Discrete Dynamics In Nature and Societymentioning

confidence: 99%

“…The solution ( , , , , ) of system (6) subject to condition (7) exists uniquely and is positive and bounded for all ∈ N. In addition, 0 < < (1 + Δ )/Δ for = 1, 2, . .…”

Section: Global Dynamics Of the Discrete Model (6)mentioning

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%

See 2 more Smart Citations

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 first study the global dynamics of the continuous system (2) in Section 2. In Section 3, we investigate the global dynamics of discrete system (6). A brief conclusion ends the paper.…”

Section: Discrete Dynamics In Nature and Societymentioning

confidence: 99%

“…The solution ( , , , , ) of system (6) subject to condition (7) exists uniquely and is positive and bounded for all ∈ N. In addition, 0 < < (1 + Δ )/Δ for = 1, 2, . .…”

Section: Global Dynamics Of the Discrete Model (6)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Adaptive immunity has been represented by antibody immune and cytotoxic T-lymphocytes ( ) responses. The viral infection of with -having capsids were categorized by mathematical analysis [18][19][20][21][22]. There arises a significant point that diseased cells of liver discharge -which contains capsids in the form of mature viruses after being enclosed by viral envelope proteins cellular membrane and lipids [23,24].…”

Section: Introductionmentioning

confidence: 99%

Control and simulation impact on nonlinear Hepatitis-B model by using Padé-approximation based Differential Evolution

Farman

Tabassum

Saeed

et al. 2019

Preprint

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Hepatitis B is the main public health problem of the whole world. In epidemiology, mathematical models perform a key role in understanding the dynamics of infectious diseases. This paper proposes Padé approximation ( ) with Differential Evolution ( ) for obtaining solution of Hepatitis-B model which is nonlinear numerically. The proposed strategy transforms the nonlinear model into optimization problem by using Padé approximation. Initial conditions are converted into problem constraints and constraint problem become unconstraint by using penalty function.is obtained numerical solution of Hepatitis-B model by solving the established problem of optimization. There is no need to choose step lengths in proposed Padéapproximation based Differential Evolution ( ) technique and also converges to true steady state points. Finally, a convergence and error analysis evidence that the convergence speed of is greater than Non-Standard Finite Difference ( ) method for different time steps.

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“…Since the classical virus dynamic model that includes three ordinary differential equations has been proposed, 1,2 many extended virus dynamic models for studying infectious diseases have been constructed and studied. Particularly, a number of researchers have devoted their efforts in studying the global stability of those mathematical models [3][4][5][6][7][8][9][10] and references therein. For example, Manna and Chakrabarty 10 proposed and analyzed an hepatitis B virus (HBV) infection model with HBV DNA-containing capsids.…”

Section: Introductionmentioning

confidence: 99%

Threshold dynamics of a delayed virus infection model with cellular immunity and general nonlinear incidence

Geng

2018

Math Methods in App Sciences

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The goal of this paper is to investigate the dynamical behavior of a general nonlinear delayed viral infection model with cytotoxic T lymphocyte (CTL) immune response. The intrinsic growth rate of uninfected hepatocytes, incidence rate of infection, removal rate of infected hepatocytes and capsids, production and removal rate of viruses, activation rate of CTLs, and decay rate of CTLs are given by general nonlinear functions with a set of conditions on these general nonlinear functions, which make the analysis of the model more difficult. The global threshold dynamics with respect to the reproduction numbers for viral infection ℜ 0 and for CTL immune response ℜ 1 have been presented by constructing suitable Lyapunov functionals. Numerical simulations are carried out for a model with specific forms of the general functions to confirm the theoretical results and show that both the numerical and theoretical results are consistent.

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Global stability of one and two discrete delay models for chronic hepatitis B infection with HBV DNA-containing capsids

Cited by 42 publications

References 26 publications

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

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

Control and simulation impact on nonlinear Hepatitis-B model by using Padé-approximation based Differential Evolution

Threshold dynamics of a delayed virus infection model with cellular immunity and general nonlinear incidence

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