Discretization and dynamic consistency of a delayed and diffusive viral infection model

Geng, Yan; Xu, Jin; Hou, Jiangyong

doi:10.1016/j.amc.2017.08.041

Cited by 30 publications

(14 citation statements)

References 19 publications

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“…Numerical modeling involves the study of methods to find approximate solutions to differential equations. In recent times, numerical solutions of delay differential equations are of great import due to the versatility of the modeling processes in different fields [42][43][44][45][46][47][48]. Various physical systems involving delay differential equations possesses the physical phenomenon like population sizes, concentration, density and pressure etc.…”

Section: Numerical Modelingmentioning

confidence: 99%

Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay

et al. 2020

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This study is concerned with finding a numerical solution to the delay epidemic model with diffusion. This is not a simple task as variables involved in the model exhibit some important physical features. We have therefore designed an efficient numerical scheme that preserves the properties acquired by the given system. We also further develop Euler's technique for a delayed epidemic reaction-diffusion model. The proposed numerical technique is also compared with the forward Euler technique, and we observe that the forward Euler technique demonstrates the false behavior at certain step sizes. On the other hand, the proposed technique preserves the true behavior of the continuous system at all step sizes. Furthermore, the effect of the delay factor is discussed graphically by using the proposed technique.

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Section: Numerical Modelingmentioning

confidence: 99%

Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay

et al. 2020

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“…Mathematical modeling of viral dynamics with cell‐free infection have received wide attentions . Let T ( t ), T I ( t ), and V ( t ) represent concentrations of uninfected cells, infected cells, and virus at time t , respectively.…”

Section: Introductionmentioning

confidence: 99%

Global analysis of a diffusive viral model with cell‐to‐cell infection and incubation period

Wang

Guo

et al. 2020

Math Methods in App Sciences

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We propose a diffusive viral model incorporating cell-to-cell infection mode, nonlinear incidences, incubation period, and spatial heterogeneity. For the spatially heterogeneous model, we derive the extinction/persistence result by the basic reproduction number  0 . For the spatially homogeneous model, we study global stabilities of steady states by establishing Lyapunov functions. The existing method for studying global stabilities of diffusive viral models has been generalized, which weakens the required conditions. Some existing results can be covered and improved. A specific example is given to illustrate the general results. In addition, we show that  0 is underestimated if we neglect incubation period of infected cells.

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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%

“…Recently, nonlinear incidence form has been taken into consideration in viral infection models as kH (V). 6,18 Of course, several other incidence forms have been included in viral infection models (see previous studies 7,16,17 and references therein). In addition, notice that the death rates of the five compartments and the production rate of viruses presented in model (2) are given by linear functions; moreover, the activation rate of CTLs and the removal rate of the infection hepatocytes by CTLs are given by specific forms.…”

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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Discretization and dynamic consistency of a delayed and diffusive viral infection model

Cited by 30 publications

References 19 publications

Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay

Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay

Global analysis of a diffusive viral model with cell‐to‐cell infection and incubation period

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

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