Global asymptotic stability of a delay differential equation model for SARS-CoV-2 virus infection mediated by ACE2 receptor protein

Lv, Jinlong; Ma, Wanbiao

doi:10.1016/j.aml.2023.108631

Cited by 10 publications

(19 citation statements)

References 17 publications

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“…In [24][25][26], the authors deal with the uncertainties present by introducing stochasticity. Global stability is studied, for example, in [27,28] and for models with delay in [29,30]. The bifurcation of solutions is analyzed in [31,32], and many papers also perform bifurcation numerical calculations using DDE-BIFTOOL [33].…”

Section: Introductionmentioning

confidence: 99%

A Model of Hepatitis B Viral Dynamics with Delays

Chen-Charpentier

2024

AppliedMath

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Hepatitis B is a liver disease caused by the human hepatitis B virus (HBV). Mathematical models help further the understanding of the processes involved and help make predictions. The basic reproduction number, R0, is an index that predicts whether the disease will be chronic or not. This is the single most-important information that a mathematical model can give. Within-host virus processes involve delays. We study two within-host hepatitis B virus infection models without and with delay. One is a standard one, and the other considering additional processes and with two delays is new. We analyze the basic reproduction number and alternative threshold indices. The values of R0 and the alternative indices change depending on the model. All these indices predict whether the infection will persist or not, but they do not give the same rate of growth of the infection when it is starting. Therefore, the choice of the model is very important in establishing whether the infection is chronic or not and how fast it initially grows. We analyze these indices to see how to decrease their value. We study the effect of adding delays and how the threshold indices depend on how the delays are included. We do this by studying the local asymptotic stability of the disease-free equilibrium or by using an equivalent method. We show that, for some models, the indices do not change by introducing delays, but they change when the delays are introduced differently. Numerical simulations are presented to confirm the results. Finally, some conclusions are presented.

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Section: Introductionmentioning

confidence: 99%

A Model of Hepatitis B Viral Dynamics with Delays

Chen-Charpentier

2024

AppliedMath

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“…A n s +A n , where A s is the half-saturation constant and n is the Hill coefficient [34], [37]. The function Ψ(A) is continuously differentiable on [0, +∞) and strictly monotonically increasing.…”

Section: Model Formulationmentioning

confidence: 99%

“…The local stability of an ODE system for SARS-CoV-2 infection in the ACE2 receptor was studied by Chatterjee and Al Basir [33]. Lv and Ma [34] proposed a system of delay differential equations (DDEs) for SARS-CoV-2 infection mediated by ACE2 receptor as:…”

Section: Introductionmentioning

confidence: 99%

“…The variable A = A(t) represents the concentration of per unit volume of ACE2 receptors at time t. Ψ(A) represents the probability of successful entry of the virion into the epithelial cell mediated by the receptor ACE2. When the concentration of the epithelial cell receptor ACE2 is lower (higher), there are Ψ(A) ∼ 0(∼ 1) [34].…”

Section: Introductionmentioning

confidence: 99%

“…This can provide us with a better understanding of the virus's dynamics and how the immune system controls and clears it. Local and/or global stability of different within-host SARS-CoV-2 infection models were investigated in several works (see [11], [18], [19], [21], [27], [33], [34], [35] and [36]).…”

Section: Introductionmentioning

confidence: 99%

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Global Stability of a Delayed Model for the Interaction of SARS-CoV-2/ACE2 and Adaptive Immunity

Elaiw,

Alsulami,

Hobiny

2024

Int. J. Anal. Appl.

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The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the culprit behind the coronavirus disease 2019 (COVID-19), which has killed millions of people. SARS-CoV-2 binds its spike (S) protein to the angiotensin-converting enzyme 2 (ACE2) receptor to inter the epithelial cells in the respiratory tracts. ACE2 is a crucial mediator in the SARS-CoV-2 infection pathway. In this paper, we construct a mathematical model to describe the SARS-CoV-2/ACE2 interaction and the adaptive immunological response. The model predicts the effects of latently infected cells as well as immunological responses from cytotoxic T lymphocytes (CTLs) and antibodies. The model is incorporated with three distributed time delays: (i) delay in the formation of latently infected epithelial cells, (ii) delay in the activation of latently infected epithelial cells, (iii) delay in the maturation of new released SARS-CoV-2 virions. We show that the model is well-posed and it admits five equilibria. The stability and existence of the equilibria are precisely controlled by four threshold parameters Ri, i=0,1,2,3. By formulating suitable Lyapunov functions and applying LaSalle's invariance principle, we show the global asymptotic stability for all equilibria. To demonstrate the theoretical results, we conduct numerical simulations. We do sensitivity analysis and identify the most sensitive parameters. We look at how the latent phase, ACE2 receptors, antibody and CTL responses, time delays affect the dynamical behavior of SARS-CoV-2. Although the basic reproduction number R0 is unaffected by the parameters of antibody and CTL responses, it is shown that viral replication can be hampered by immunological activation of antibody and CTL responses. Further, our findings indicate that R0 is affected by the rates at which the ACE2 receptor grows and degrades. This could provide valuable guidance for the development of receptor-targeted vaccines and medications. Furthermore, it is shown that, increasing time delays can effectively decrease R0 and then inhibit the SARS-CoV-2 replication. Finally, we show that, excluding the latently infected cells in the model would result in an overestimation of R0.

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Dynamic analysis of a SIS epidemic model with nonlinear incidence and ratio dependent pulse control

Zhu,

Zhang

2024

J. Appl. Math. Comput.

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Global asymptotic stability of a delay differential equation model for SARS-CoV-2 virus infection mediated by ACE2 receptor protein

Cited by 10 publications

References 17 publications

A Model of Hepatitis B Viral Dynamics with Delays

A Model of Hepatitis B Viral Dynamics with Delays

Global Stability of a Delayed Model for the Interaction of SARS-CoV-2/ACE2 and Adaptive Immunity

Dynamic analysis of a SIS epidemic model with nonlinear incidence and ratio dependent pulse control

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