International Journal of Discrete Mathematics

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Computer Simulations of Regulatory Mechanisms of Hepatocyte with Hepatitis B Viruses Interconnected Dynamics

Received: 13 February 2019    Accepted: 13 March 2019    Published: 10 April 2019
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Abstract

The study of the functioning of hepatitis B viruses in the liver cell using methods of mathematical modeling is considered one of the topical issues. In this article, the results on identifying of areas of regimes of the functional-differential equations of the mathematical model of regulatory mechanisms of hepatocyte with hepatitis B viruses (HBV) were presented. Characteristic modes of the regulatory of the interrelated activity of the molecular genetic mechanisms of the liver cells and viruses of hepatitis B are analyzed. The features of the area of the chaotic regime regulatory related activities of molecular genetic mechanisms of the hepatocyte and HBV by analyzing the dynamics of the Lyapunov exponent. Defined small regions with regular behavior - "r-windows" in the field of dynamic chaos. The regulatory of the hepatocyte and HBV can be moved from the region of dynamic chaos to normal region by using "r-windows". The results of the computational experiment on the quantitative analysis of the regulatory of liver cell and HBV are presented.

DOI 10.11648/j.dmath.20190401.15
Published in International Journal of Discrete Mathematics (Volume 4, Issue 1, June 2019)
Page(s) 32-37
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Regulatory Mechanisms, Mathematical and Computer Models, Qualitative and Quantitative Analysis, Chaos, Black Hole

References
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[3] I. A. Moneim and H. A. Khalil (2015). Modeling and Simulation of the Spread of HBV Disease with Infectious Latent, J. Appl. Math. 6: pp. 745-753. Available at http://dx.doi.org/10.4236/am.2015.65070
[4] E. N. Wiah, I. A. Adetunde and L. Brew (2012). Mathematical Modeling of the Interaction of Hepatitis B Virus with the Immune System Including the Effect of Therapy, Int. J. Mod. Math. Sci. 1(2): pp. 53-72.
[5] A. M. Elaiw, M. A. Alghamdi and Sh. Aly (2013). Hepatitis B Virus Dynamics: Modeling, Analysis, and Optimal Treatment Scheduling, Disc. Dyn. in Nat. and Soc. 9.
[6] X. Chen, K. Sun, J. Qiu, X. Chen, Ch. Yang and A. Zhang (2014). Dynamics analysis of an amended HBV infection model with a simulation for anti-HBV infection therapy, in Proceedings of the 33rd Chinese Control Conference. Nanjing. China. pp. 2829-2834.
[7] K. Mboya, D. O. Makinde, E. S. Massawe (2015). Cytotoxic Cells and Control Strategies are Effective in Reducing the HBV Infection through a Mathematical Modelling, Int. J. Prevent. and Treat. 4(3): pp. 48-57.
[8] M. C. Stanca, M. R. Ruy and S. P. Alan (2014). Antibody Responses during Hepatitis B Viral Infection, PLoS Comput. Biol. 10(7): pp. 1-16.
[9] H. Laarabi, A. Abta, M. Rachik and J. Rouyaghroumni (2013). Optimal antiviral treatment strategies of HBV infection model with logistic hepatocytes growth, ISRN Biomath.
[10] B. N. Hidirov (2014). Selected works on mathematical modeling of the regulatory of living systems, Publishing House, Moscow, Izhevsk.
[11] B. N. Hidirov and A. M. Turgunov (2010). Mathematical modeling of regulatory mechanisms for the development of viral hepatitis B, Sci. J. Prob. Comput. and Appl. Math. 125: pp. 153-160.
[12] B. N. Hidirov and A. M. Turgunov (2012). Modeling of molecular genetics mechanisms of control of viral hepatitis B, Uzb. J. Prob. Inf. and Ener. 2-3: pp. 13-18.
[13] M. Saidalieva, M. B. Hidirova and A. M. Turgunov (2014). Areas of homogeneous solutions of the equations of the mathematical model of the regulatory of liver in hepatitis B, Uzb. J. Prob. Inf. and Ener. 6: pp. 3-8.
[14] A. M. Turgunov (2017). Characteristic regimes of the behavior of solutions of the regulatorika equations of the "Hepatocyte-HBV" system, in Mat. XVII Int. Sci. and Meth. Conf. "Informatics: Problems, Methodology, Technologies". 2: pp. 446-450.
[15] M. B. Hidirova and A. M. Turgunov (2015). Computer modeling of infectious disease with viral hepatitis B using information technologies, in Mat. XVII Int. Sci. and Meth. Conf. "Informatics: Problems, Methodology, Technologies", 1: pp. 478-481.
[16] M. Saidalieva, M. B. Hidirova and A. M. Turgunov (2015). Modeling of the regulatory of the liver cell in the quasi-stationary state of the hepatitis B virus, TUIT BULLETIN 3(35): pp. 160-165.
[17] M. B. Hidirova, M. Saydalieva and A. M. Turgunov (2016). Analysis of the molecular and genetic mechanisms of liver cells under a load of its viruses hepatitis "B", in Sci. Art. Int. Sci. Prac. Conf. "INNOVATION-2016". pp. 268-269.
[18] A. M. Turgunov (2017). On the modeling of regulatory of the liver cell and hepatitis B viruses, Sci. J. Prob. Comput. and Appl. Math. 4(10): pp. 53-62.
[19] A. M. Turgunov (2017). Analysis of the regulatory of the liver cell and hepatitis B viruses using a computer model, in Collec. Rep. Repub. Sci. Tech. Conf. IICTIDRSE, 1: pp. 263-265.
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[24] M. B. Hidirova (2014). On the solutions of the functional differential equation of the regulatory of living systems, Bul. Moscow Univ. Math. Mech. 1: pp. 50-52.
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Author Information
  • Scientific and Innovation Center of Information and Communication Technologies, Tashkent University of Information Technologies Named After Muhammad Al-Khwarizmi, Tashkent, Uzbekistan

  • Scientific and Innovation Center of Information and Communication Technologies, Tashkent University of Information Technologies Named After Muhammad Al-Khwarizmi, Tashkent, Uzbekistan

  • Scientific and Innovation Center of Information and Communication Technologies, Tashkent University of Information Technologies Named After Muhammad Al-Khwarizmi, Tashkent, Uzbekistan

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  • APA Style

    Mahruy Saidalieva, Mohiniso Baxromovna Hidirova, Abrorjon Maxamatsoliyevich Turgunov. (2019). Computer Simulations of Regulatory Mechanisms of Hepatocyte with Hepatitis B Viruses Interconnected Dynamics. International Journal of Discrete Mathematics, 4(1), 32-37. https://doi.org/10.11648/j.dmath.20190401.15

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    ACS Style

    Mahruy Saidalieva; Mohiniso Baxromovna Hidirova; Abrorjon Maxamatsoliyevich Turgunov. Computer Simulations of Regulatory Mechanisms of Hepatocyte with Hepatitis B Viruses Interconnected Dynamics. Int. J. Discrete Math. 2019, 4(1), 32-37. doi: 10.11648/j.dmath.20190401.15

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    AMA Style

    Mahruy Saidalieva, Mohiniso Baxromovna Hidirova, Abrorjon Maxamatsoliyevich Turgunov. Computer Simulations of Regulatory Mechanisms of Hepatocyte with Hepatitis B Viruses Interconnected Dynamics. Int J Discrete Math. 2019;4(1):32-37. doi: 10.11648/j.dmath.20190401.15

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  • @article{10.11648/j.dmath.20190401.15,
      author = {Mahruy Saidalieva and Mohiniso Baxromovna Hidirova and Abrorjon Maxamatsoliyevich Turgunov},
      title = {Computer Simulations of Regulatory Mechanisms of Hepatocyte with Hepatitis B Viruses Interconnected Dynamics},
      journal = {International Journal of Discrete Mathematics},
      volume = {4},
      number = {1},
      pages = {32-37},
      doi = {10.11648/j.dmath.20190401.15},
      url = {https://doi.org/10.11648/j.dmath.20190401.15},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.dmath.20190401.15},
      abstract = {The study of the functioning of hepatitis B viruses in the liver cell using methods of mathematical modeling is considered one of the topical issues. In this article, the results on identifying of areas of regimes of the functional-differential equations of the mathematical model of regulatory mechanisms of hepatocyte with hepatitis B viruses (HBV) were presented. Characteristic modes of the regulatory of the interrelated activity of the molecular genetic mechanisms of the liver cells and viruses of hepatitis B are analyzed. The features of the area of the chaotic regime regulatory related activities of molecular genetic mechanisms of the hepatocyte and HBV by analyzing the dynamics of the Lyapunov exponent. Defined small regions with regular behavior - "r-windows" in the field of dynamic chaos. The regulatory of the hepatocyte and HBV can be moved from the region of dynamic chaos to normal region by using "r-windows". The results of the computational experiment on the quantitative analysis of the regulatory of liver cell and HBV are presented.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Computer Simulations of Regulatory Mechanisms of Hepatocyte with Hepatitis B Viruses Interconnected Dynamics
    AU  - Mahruy Saidalieva
    AU  - Mohiniso Baxromovna Hidirova
    AU  - Abrorjon Maxamatsoliyevich Turgunov
    Y1  - 2019/04/10
    PY  - 2019
    N1  - https://doi.org/10.11648/j.dmath.20190401.15
    DO  - 10.11648/j.dmath.20190401.15
    T2  - International Journal of Discrete Mathematics
    JF  - International Journal of Discrete Mathematics
    JO  - International Journal of Discrete Mathematics
    SP  - 32
    EP  - 37
    PB  - Science Publishing Group
    SN  - 2578-9252
    UR  - https://doi.org/10.11648/j.dmath.20190401.15
    AB  - The study of the functioning of hepatitis B viruses in the liver cell using methods of mathematical modeling is considered one of the topical issues. In this article, the results on identifying of areas of regimes of the functional-differential equations of the mathematical model of regulatory mechanisms of hepatocyte with hepatitis B viruses (HBV) were presented. Characteristic modes of the regulatory of the interrelated activity of the molecular genetic mechanisms of the liver cells and viruses of hepatitis B are analyzed. The features of the area of the chaotic regime regulatory related activities of molecular genetic mechanisms of the hepatocyte and HBV by analyzing the dynamics of the Lyapunov exponent. Defined small regions with regular behavior - "r-windows" in the field of dynamic chaos. The regulatory of the hepatocyte and HBV can be moved from the region of dynamic chaos to normal region by using "r-windows". The results of the computational experiment on the quantitative analysis of the regulatory of liver cell and HBV are presented.
    VL  - 4
    IS  - 1
    ER  - 

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