Volume 4, Issue 1, June 2019, Page: 32-37
Computer Simulations of Regulatory Mechanisms of Hepatocyte with Hepatitis B Viruses Interconnected Dynamics
Mahruy Saidalieva, Scientific and Innovation Center of Information and Communication Technologies, Tashkent University of Information Technologies Named After Muhammad Al-Khwarizmi, Tashkent, Uzbekistan
Mohiniso Baxromovna Hidirova, Scientific and Innovation Center of Information and Communication Technologies, Tashkent University of Information Technologies Named After Muhammad Al-Khwarizmi, Tashkent, Uzbekistan
Abrorjon Maxamatsoliyevich Turgunov, Scientific and Innovation Center of Information and Communication Technologies, Tashkent University of Information Technologies Named After Muhammad Al-Khwarizmi, Tashkent, Uzbekistan
Received: Feb. 13, 2019;       Accepted: Mar. 13, 2019;       Published: Apr. 10, 2019
DOI: 10.11648/j.dmath.20190401.15      View  14      Downloads  7
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.
Keywords
Regulatory Mechanisms, Mathematical and Computer Models, Qualitative and Quantitative Analysis, Chaos, Black Hole
To cite this article
Mahruy Saidalieva, Mohiniso Baxromovna Hidirova, Abrorjon Maxamatsoliyevich Turgunov, Computer Simulations of Regulatory Mechanisms of Hepatocyte with Hepatitis B Viruses Interconnected Dynamics, International Journal of Discrete Mathematics. Vol. 4, No. 1, 2019, pp. 32-37. doi: 10.11648/j.dmath.20190401.15
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
World Health Organization. Fact Sheet July (2016). Available at http://www.who.int/topics/hepatitis/en/
[2]
Lancet. 390 (2017). pp. 1151-1210.
[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.
[20]
R. Bellman and K. Cooke (1963). Differential Difference Equations, Publishing House, Academic Press.
[21]
J. Hale (1984). Theory of Functional Differential Equations, Publishing House, Moscow, The World.
[22]
V. G. Pimenov (2008). Functional-differential equations in biology and medicine, Publishing House, Tutorial, Ekaterinburg.
[23]
G. Hall and J. M. Watt (1976). Modern Numerical Methods for Ordinary Differential Equations, Publishing House, Clarendon Press, Oxford.
[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.
[25]
B. N. Hidirov, M. Saidalieva and M. B. Hidirova (2009). Program for qualitative analysis of functional differential equations of regulatory, The software product is inspected by the State Patent Office of the Republic of Uzbekistan on 18.12.2009. Cer. Num. DGU 01879.
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