Using Mathematical Model to Depict the Immune Response to Hepatitis B Virus Infection

Wiah, Eric Neebo; Dontwi, I. K.; Adetunde, I. A.

doi:10.5539/jmr.v3n2p157

Cited by 9 publications

(8 citation statements)

References 19 publications

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“…The simulation analysis shows that at all the stages of immune response to viral infections, the cells of the immune system considered increase as viral load decreases which agrees with the three categories of viral loads of the study of Hancioglu et al (2007). In summary, the stability analysis in the current study is in consistent with the results of Anderson and May (1992), Bittner and Wahl (2000), Wodarz (2004), Hancioglu et al (2007), Wiah et al (2011), Nakata (2011 and Tian and Wang (2015).…”

Section: Discussionsupporting

confidence: 88%

“…The categories with their corresponding viral loads also corresponds to the continuous reduction of viral load at the various stages of this current study. The results of the study of Wiah et al (2011) showed the existence of disease free and endemic equilibrium states. The analysis of the adaptive immune response stage of this same study showed that with sufficient antibody response with enough specificity, the dynamics is able to restore the health of the host irrespective of the intensity of the innate response.…”

Section: Discussionmentioning

confidence: 98%

“…Long et al (2008), also worked on a Mathematical Modeling of Cytotoxic Lymphocyte-Mediated Immune Response to Hepatitis B Virus Infection in which the Human Immunodeficiency Virus (HIV) infection was successfully to simulate the interaction between HIV and cytotoxic lymphocyte mediated immune response and also considered the indicator of the liver cell damage between Hepatitis B and the cytotoxic mediated immune response and the indicator of the liver cell damage. Wiah et al (2011) presented a mathematical model of immune response to Hepatitis B Virus (HBV) infection which focuses on the control of the infection by the interferons, innate and adaptive immunity. Nakata (2011) published study on the global dynamics of a cell mediated immunity in viral infection models with distributed delays which admitted three possible equilibria states.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Model of the Behaviour of T Cytotoxic, T Helper, B and Natural Killer Cells in the Presence of Viruses

Adusei¹,

Frempong²,

Darkwah³

et al. 2015

J. of Medical Sciences

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The behaviour of lymphoid cells in the absence of viruses has already been published in the year 2013. This study is a continuation of recent attempts to understand, via mathematical modeling, the behavior of lymphoid cells in the absence and in the presence of viruses. In this study, which is the behaviour of lymphoid cells in the presence of viruses will be treated in three respects. Firstly, the innate immune response stage, secondly, the overlap of innate and adaptive immune responses stage and finally, the adaptive immune response stage of viral infections. The adaptive immune response stage considers the viremia and cell-mediated immune responses stage. The steady states and the stability for these differential models are deduced. Each of the models permit the existence of two types of stationary states. There is the state of no infection, with no virus cells while the other is the state of co-existence where a virus cell persists against the background of immune response. The state of no infection is asymptotically stable and a state of infection is unstable. It is found from the study that the state of no infection represents the preparedness of the immune state prior to the infection. Numerical simulation analysis suggests that the cells (NK, T c , T h and B) grow exponentially as a result of proliferation and saturation because of the contacts between them and reach therefore reach plateau as time (t) increases. These immune cells are able to reduce viral load to the barest minimum if not reducing it to zero.

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Section: Discussionsupporting

confidence: 88%

Section: Discussionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Mathematical Model of the Behaviour of T Cytotoxic, T Helper, B and Natural Killer Cells in the Presence of Viruses

Adusei¹,

Frempong²,

Darkwah³

et al. 2015

J. of Medical Sciences

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“…Type-2 interferons IFN-γ, denoted as F 2 (t), are produced by CTLs and NKs (natural killer cells) N (t) [12,13,35,36] at rates p 2 and p 3 , respectively, and they are lost at a rate δ 2 . Both types of interferons have the capacity to render the uninfected cells protected from infection through making them resistant to infection [19,37,38], or by turning them into refractory cells [18,39]. Therefore, the combined effect of interferons making uninfected cells refractory is taken to be ϕ 1 (F 1 + F 2 ) per uninfected cell, and refractory cells can lose their viral resistance at a rate ρ [20].…”

Section: Model Derivationmentioning

confidence: 99%

Mathematical model of immune response to hepatitis B

Chenar

Kyrychko

Blyuss

2018

Journal of Theoretical Biology

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A new detailed mathematical model for dynamics of immune response to hepatitis B is proposed, which takes into account contributions from innate and adaptive immune responses, as well as cytokines. Stability analysis of different steady states is performed to identify parameter regions where the model exhibits clearance of infection, maintenance of a chronic infection, or periodic oscillations. Effects of nucleoside analogues and interferon treatments are analysed, and the critical drug efficiency is determined.

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“…Application of the mathematical models to different parameters shows that some patients get cleared of the virus quickly due to drug therapy, whereas in case of other patients the drug therapy works much slower [12]. Therefore, in some cases treatment has to be stopped.…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions for HBV infection with stability analysis using LHAM during antiviral therapy

Aniji¹,

Kavitha²,

Balamuralitharan

2020

Bound Value Probl

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Hepatitis B virus (HBV) is a life-threatening virus that causes very serious liver-related diseases from the family of Hepadnaviridae having very rare qualities resembling retroviruses. In this paper, we analyze the effect of antiviral therapy through mathematical modeling by using Liao's homotopy analysis method (LHAM) that defines the connection between the target liver cells and the HBV. We also examine the basic nonlinear differential equation by LHAM to get a semi-analytical solution. This can be a very straight and direct method which provides the appropriate solution. Moreover, the local and global stability analysis of disease-free and endemic equilibrium is done using Lyapunov function. Mathematica 12 software is used to find out the solutions and graphical representations. We also discuss the numerical simulations up to sixth-order approximation and error analysis using the same software.

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Using Mathematical Model to Depict the Immune Response to Hepatitis B Virus Infection

Cited by 9 publications

References 19 publications

Mathematical Model of the Behaviour of T Cytotoxic, T Helper, B and Natural Killer Cells in the Presence of Viruses

Mathematical Model of the Behaviour of T Cytotoxic, T Helper, B and Natural Killer Cells in the Presence of Viruses

Mathematical model of immune response to hepatitis B

Approximate solutions for HBV infection with stability analysis using LHAM during antiviral therapy

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