Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids

Manna, Kalyan; Chakrabarty, Siddhartha P.

doi:10.1080/10236198.2015.1056524

Cited by 44 publications

(23 citation statements)

References 34 publications

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“…Consequently, from (26)- (28) we have sgn(U 1 -U 2 ) = sgn(U 2 -U 1 ), which is a contradiction. This implies that…”

Section: Global Stabilitymentioning

confidence: 93%

“…For example, Geng et al [27] considered the mobility of capsids and viruses and applied the nonstandard finite difference (NSFD) scheme to discretize a continuous HBV infection model with capsids. Their work was an extension to the work of Manna and Chakrabarty [28]. Guo et al [29] studied an HBV infection model which contains three time delays, capsids, general incidence rate, and allows the movement of viruses by diffusion.…”

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confidence: 99%

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Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

Ełaiw

Agha

2019

Adv Differ Equ

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This paper studies the global dynamics of a general diffusive hepatitis B virus (HBV) infection model. The model includes both enveloped viruses and DNA containing capsids. Two immune responses are recruited to attack the virus and infected hepatocytes. These are the cytotoxic T-lymphocytes (CTL) which kill the infected liver cells, and B cells which send antibodies to attack the virus. The non-negativity and boundedness of the solutions are discussed. The existence of spatially homogeneous equilibrium points is examined. The global stability of all possible equilibrium points is proved by choosing suitable Lyapunov functionals. Some numerical simulations are performed to enhance the theoretical results and present the behavior of solutions in space and time.

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“…Consequently, from (26)- (28) we have sgn(U 1 -U 2 ) = sgn(U 2 -U 1 ), which is a contradiction. This implies that…”

Section: Global Stabilitymentioning

confidence: 93%

mentioning

confidence: 99%

Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

Ełaiw

Agha

2019

Adv Differ Equ

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“…(13) ℎ 1 ( ) = ( ) -0 = 0 (14) ℎ 2 ( ) = ( ) -0 = 0 (15) ℎ 3 ( ) = ( ) -0 = 0 (16) ℎ 4 ( ) = ( ) -0 = 0 (17) ℎ 5 ( ) = ( ) -0 = 0 (18) ℎ 6 ( ) = ( ) -0 = 0 The inequality constraints (19) to (24) are related to positivity ,…”

Section: Problem Constraintsmentioning

confidence: 99%

“…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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“…However, how to select a proper discrete method so that the global properties of solutions of the corresponding continuous models can be efficiently preserved is still an open problem [14]. Recently, Mickens has made an attempt in this regard, by proposing a robust nonstandard finite difference (NSFD) scheme [15,16], which has been widely employed in the study of different kinds of epidemic models and one important advantage of Mickens' method is that it can be more efficient in preserving the global dynamics to the corresponding continuous epidemic models [10,[17][18][19][20][21][22][23]. However, there is no result about discrete viral infection model with time delays and immune response.…”

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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Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids

Cited by 44 publications

References 34 publications

Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

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

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

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