In this article, we will present the results of the stability analysis of the equilibrium point of the mathematical model of the regulatory of the interrelated activity of the hepatocyte and hepatitis B viruses. The analysis of this model used the conditions of the Hayes criterion. In this study, the general condition of the Hayes criterion is obtained. If the general condition of the Hayes criterion is satisfied, then the equilibrium point is stable. If the general condition of the Hayes criterion is not fulfilled, then the equilibrium point is not stable, and hence thiscan describe modes "limit cycle", "chaos" and "black hole" mathematical models of the interrelated activity of the liver cell and hepatitis B viruses. The results of the computational experiment on the quantitative analysis of the regulatory of liver cell and HBV are presented.
Published in | International Journal of Biomedical Materials Research (Volume 6, Issue 1) |
DOI | 10.11648/j.ijbmr.20180601.11 |
Page(s) | 1-7 |
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), 2018. Published by Science Publishing Group |
Regulatory, Mathematics Model, Equilibrium Points, Stability, Qualitative and Quantitative Analysis
[1] | World Health Organization (2016). Fact Sheet, July, Available at http://www.who.int/topics/hepatitis/en/. |
[2] | Perova I. G., Khludeeva O. I. (2015). Management of the development of infectious diseases. System of information boxes. 1 (126): 174-176. |
[3] | Lancet 2017. 390: 1151–210. http://www.thelancet.com/journals/lancet/article/PIIS0140-6736 (17)32152-9/fulltext. |
[4] | Sunbul M. (2014). Hepatitis B virus genotypes: global distribution and clinical importance. World J. Gastroenterology. 20 (18): 5427-5434. |
[5] | Abu O., Onalo S. E. (2017). Numerical Analysis of a Mathematical Model of Hepatitis B Virus Transmission Dynamics in the Presence of Vaccination and Treatment. Journal of Scientific and Engineering Research. 4 (9): 295-310. |
[6] | Moneim I. A., Khalil H. A. (2015). Modeling and Simulation of the Spread of HBV Disease with Infectious Latent. Applied Mathematics. 6: 745-753. http://dx.doi.org/10.4236/am.2015.65070 |
[7] | Hidirov B. N., Turgunov A. M. (2012). Modeling of molecular genetics mechanisms of control of viral hepatitis B. Uzbek journal of the Problems of Informatics and Energetics. 2-3: 13-18. |
[8] | Saidalieva M., Hidirova M. B., Turgunov A. M. (2014). Areas of homogeneous solutions of the equations of the mathematical model of the regulatory of liver in hepatitis B. Uzbek journal of the Problems of Informatics and Energetics. 6: 3-8. |
[9] | Hidirova M. B., Turgunov A. M. (2015). Computer modeling of infectious disease with viral hepatitis B using information technologies. Materials of the XV International Scientific and Methodical Conference "Informatics: Problems, Methodology, Technologies". 1: 478-481. |
[10] | Hidirova M. B., Saydalieva M., Turgunov A. M. (2016). Analysis of the molecular and genetic mechanisms of liver cells under a load of its viruses hepatitis "B". Scientific articles International scientific-practical conference "INNOVATION-2016": 268-269. |
[11] | Turgunov A. M. (2017). On the modeling of regulatory of the liver cell and hepatitis B viruses. Scientific journal "Problems of computational and applied mathematics". 4 (10): 53-62. |
[12] | Turgunov A. M. (2017). Characteristic regimes of the behavior of solutions of the regulator equations of the "Hepatocyte-HBV" system. Materials of the XVII International Scientific and Methodical Conference "Informatics: Problems, Methodology, Technologies". 2: 446-450. |
[13] | Saidalieva M., Hidirova M. B., Turgunov A. M. (2015). Modeling of the regulatory of the liver cell in the quasi-stationary state of the hepatitis B virus. Scientific - technical and information-analytical journal TUIT - TUIT BULLETIN. 3 (35)/2015: 160-165. |
[14] | Hale J. (1984). Theory of Functional Differential Equations. M. The World. 421. |
[15] | Pimenov V. G. (2008). Functional-differential equations in biology and medicine. Tutorial. Ekaterinburg. 92. |
[16] | Hall G., Watt J. M. (1976). Modern Numerical Methods for Ordinary Differential Equations. Clarendon Press. Oxford. 312. |
[17] | Turgunov A. (2017). Analysis of the regulatory of the liver cell and hepatitis B viruses using a computer model. Collection of reports of the republican scientific and technical conference "The importance of information and communication technologies in the innovative development of real sectors of the economy". 1: 263-265. |
APA Style
Mohiniso Baxromovna Hidirova, Abrorjon Maxamatsoliyevich Turgunov. (2018). Analysis of Regulatory of Interrelated Activity of Hepatocyte and Hepatitis B Viruses. International Journal of Biomedical Materials Research, 6(1), 1-7. https://doi.org/10.11648/j.ijbmr.20180601.11
ACS Style
Mohiniso Baxromovna Hidirova; Abrorjon Maxamatsoliyevich Turgunov. Analysis of Regulatory of Interrelated Activity of Hepatocyte and Hepatitis B Viruses. Int. J. Biomed. Mater. Res. 2018, 6(1), 1-7. doi: 10.11648/j.ijbmr.20180601.11
AMA Style
Mohiniso Baxromovna Hidirova, Abrorjon Maxamatsoliyevich Turgunov. Analysis of Regulatory of Interrelated Activity of Hepatocyte and Hepatitis B Viruses. Int J Biomed Mater Res. 2018;6(1):1-7. doi: 10.11648/j.ijbmr.20180601.11
@article{10.11648/j.ijbmr.20180601.11, author = {Mohiniso Baxromovna Hidirova and Abrorjon Maxamatsoliyevich Turgunov}, title = {Analysis of Regulatory of Interrelated Activity of Hepatocyte and Hepatitis B Viruses}, journal = {International Journal of Biomedical Materials Research}, volume = {6}, number = {1}, pages = {1-7}, doi = {10.11648/j.ijbmr.20180601.11}, url = {https://doi.org/10.11648/j.ijbmr.20180601.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijbmr.20180601.11}, abstract = {In this article, we will present the results of the stability analysis of the equilibrium point of the mathematical model of the regulatory of the interrelated activity of the hepatocyte and hepatitis B viruses. The analysis of this model used the conditions of the Hayes criterion. In this study, the general condition of the Hayes criterion is obtained. If the general condition of the Hayes criterion is satisfied, then the equilibrium point is stable. If the general condition of the Hayes criterion is not fulfilled, then the equilibrium point is not stable, and hence thiscan describe modes "limit cycle", "chaos" and "black hole" mathematical models of the interrelated activity of the liver cell and hepatitis B viruses. The results of the computational experiment on the quantitative analysis of the regulatory of liver cell and HBV are presented.}, year = {2018} }
TY - JOUR T1 - Analysis of Regulatory of Interrelated Activity of Hepatocyte and Hepatitis B Viruses AU - Mohiniso Baxromovna Hidirova AU - Abrorjon Maxamatsoliyevich Turgunov Y1 - 2018/01/16 PY - 2018 N1 - https://doi.org/10.11648/j.ijbmr.20180601.11 DO - 10.11648/j.ijbmr.20180601.11 T2 - International Journal of Biomedical Materials Research JF - International Journal of Biomedical Materials Research JO - International Journal of Biomedical Materials Research SP - 1 EP - 7 PB - Science Publishing Group SN - 2330-7579 UR - https://doi.org/10.11648/j.ijbmr.20180601.11 AB - In this article, we will present the results of the stability analysis of the equilibrium point of the mathematical model of the regulatory of the interrelated activity of the hepatocyte and hepatitis B viruses. The analysis of this model used the conditions of the Hayes criterion. In this study, the general condition of the Hayes criterion is obtained. If the general condition of the Hayes criterion is satisfied, then the equilibrium point is stable. If the general condition of the Hayes criterion is not fulfilled, then the equilibrium point is not stable, and hence thiscan describe modes "limit cycle", "chaos" and "black hole" mathematical models of the interrelated activity of the liver cell and hepatitis B viruses. The results of the computational experiment on the quantitative analysis of the regulatory of liver cell and HBV are presented. VL - 6 IS - 1 ER -