The high-order multistep ADI solver for two-dimensional nonlinear delayed reaction–diffusion equations with variable coefficients

Xie, Jianqiang; Zhang, Zhiyue

doi:10.1016/j.camwa.2018.02.017

Cited by 25 publications

(5 citation statements)

References 20 publications

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“…It is possible to extend the proposed model in several ways by considering immune response delay [21], CTL response [23,47], reaction diffusion [48,49] and memory effect [50,51].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Analysis of Humoral Immunity SARS-CoV-2 Infection Model with ACE2 Receptor and Latent Phase

Elaiw,

Alsulami,

Hobiny

2024

Contemp. Math.

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Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is RNA virus which causes the coronavirus disease 2019 (COVID-19). SARS-CoV-2 infects the epithelial (target) cells by binding its spike protein, S, to the Angiotensin-Converting Enzyme 2 (ACE2) receptor on the surface of epithelial cells. ACE2 is an essential mediating factor in the SARS-CoV-2 infection pathway. In this study, we build a mathematical model for characterizing the dynamics of SARS-CoV-2 within the host while taking into account the impact of humoral immunity and the function of the ACE2 receptor. We incorporate the cells that are latently infected into the model. We consider three distributed delays: (i) delay in development of latently infected epithelial cells, (ii) delay in the latently infected epithelium cells’ activation, and (iii) delay in the maturation of recently released SARS-CoV-2 virions. We first address the fundamental properties of the delayed system, then find all possible equilibria. We demonstrate the existence and stability of the equilibria on the basis of two threshold parameters, namely basic reproduction number (ℜ₀) and humoral immune activation number (ℜ1). By building appropriate Lyapunov functions and applying LaSalle’s invariance principle, we prove the global asymptotic stability for all equilibria. We do numerical simulations to demonstrate the theoretical conclusions. We do sensitivity analysis and determine the most vulnerable parameters. Discussion is had on how the dynamics of the SARS-CoV-2 are affected by ACE2 receptors, humoral immunity, latent phase and time delays. It is shown that vigorous activation of humoral immunity can suppress viral multiplication. We found that, ℜ₀ is influenced by the rates of ACE2 receptor growth and degradation, and this may offer valuable guidance for the creation of potential receptor-targeted vaccinations and medications. Further, it is shown that, increasing time delays can effectively decrease ℜ₀ and then inhibit the SARS-CoV-2 replication. Finally, we showed that, excluding the latently infected cells in the model would result in an overestimation of ℜ₀. Our findings may be useful in understanding the dynamics of SARS-CoV-2 infection in the host as well as in the development of novel therapies.

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“…It is possible to extend the proposed model in several ways by considering immune response delay [21], CTL response [23,47], reaction diffusion [48,49] and memory effect [50,51].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Analysis of Humoral Immunity SARS-CoV-2 Infection Model with ACE2 Receptor and Latent Phase

Elaiw,

Alsulami,

Hobiny

2024

Contemp. Math.

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“…Transmission systems, when it comes in damping form such as our model, are revealed to be very interesting in applied real sciences. These increasingly complex systems with varied functions are fertile fields of research that require extensive qualitative studies (see [10,11]). The case considered in this paper, where there is an interaction between two damping terms, has not been tackled before.…”

Section: Introduction and Position Of Problemmentioning

confidence: 99%

Decay Properties for Transmission System with Infinite Memory and Distributed Delay

Saber,

Braik,

Bahri

et al. 2024

Fractal Fract

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We consider a damped transmission problem in a bounded domain where the damping is effective in a neighborhood of a suitable subset of the boundary. Using the semigroup approach together with Hille–Yosida theorem, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.

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“…Soon afterwards, Zhang et al [27][28][29][30] extended this type of investigation to nonlinear delay convection-reaction-diffusion equations, delay parabolic equations with variable coefficient, 2D semilinear multidelay parabolic equations and non-Fickian delay reaction-diffusion equations. Moreover, Deng [31] derived a compact multistep method combined with the Richardson extrapolation for 2D nonlinear delay reaction-diffusion equations, Xie and Zhang [32] considered the error estimate of a high-order compact multistep ADI method for 2D nonlinear delay reaction-diffusion equations with variable coefficients, and Qin et al [33] studied linearized compact ADI methods for semilinear parabolic problems with distributed delay.…”

Section: Introductionmentioning

confidence: 99%

Linearized compact difference methods for solving nonlinear Sobolev equations with distributed delay

Tan

Ran

2022

Numerical Methods Partial

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This paper deals with the numerical computation and analysis for nonlinear Sobolev equations with distributed delay. We present linearized compact difference methods for solving one-and two-dimensional cases, respectively. The solvability, convergence and stability of the methods are derived and it is shown under some suitable conditions that the methods have second-order accuracy in time and fourth-order accuracy in space. Moreover, with several numerical examples, the theoretical accuracy and computational effectiveness of the proposed methods are confirmed.

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The high-order multistep ADI solver for two-dimensional nonlinear delayed reaction–diffusion equations with variable coefficients

Cited by 25 publications

References 20 publications

Analysis of Humoral Immunity SARS-CoV-2 Infection Model with ACE2 Receptor and Latent Phase

Analysis of Humoral Immunity SARS-CoV-2 Infection Model with ACE2 Receptor and Latent Phase

Decay Properties for Transmission System with Infinite Memory and Distributed Delay

Linearized compact difference methods for solving nonlinear Sobolev equations with distributed delay

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