International Journal of Biomedical Materials Research 2018; 6(1): 1-7 http://www.sciencepublishinggroup.com/j/ijbmr doi: 10.11648/j.ijbmr.20180601.11 ISSN: 2330-7560 (Print); ISSN: 2330-7579 (Online) Analysis of Regulatory of Interrelated Activity of Hepatocyte and Hepatitis B Viruses Mohiniso Baxromovna Hidirova * , Abrorjon Maxamatsoliyevich Turgunov Scientific and Innovation Center of Information and Communication Technologies, Tashkent University of Information Technologies Named After Muhammad Al-Khwarizmi, Tashkent, Uzbekistan Email address: mhidirova@yandex.ru (M. B. Hidirova), abrorjon-2017@mail.ru (A. M. Turgunov) * Corresponding author To cite this article: Mohiniso Baxromovna Hidirova, Abrorjon Maxamatsoliyevich Turgunov. Analysis of Regulatory of Interrelated Activity of Hepatocyte and Hepatitis B Viruses. International Journal of Biomedical Materials Research. Vol. 6, No. 1, 2018, pp. 1-7. doi: 10.11648/j.ijbmr.20180601.11 Received: October 25, 2017; Accepted: November 16, 2017; Published: January 16, 2018 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. Keywords: Regulatory, Mathematics Model, Equilibrium Points, Stability, Qualitative and Quantitative Analysis 1. Introduction Hepatitis B is a viral infection that affects the liver. According to WHO estimates, 240 million people are chronically infected with the hepatitis B virus (HBV) [1]. Currently, this virus remains the third most common after diseases like cardiovascular system and oncological pathologies [2]. Approximately 19.4% of deaths in recent years have been caused by infections, and this is gradually increasing. The most deadly virus on the earth was various strains of the hepatitis virus, which kills more than 1.3 million people every year. The mortality from hepatitis increased by about 22% compared with HIV, tuberculosis and malaria. One of the reasons for this is that people do not even know that they have a virus. According to researchers, only 5% of developed and developing countries are aware of their diagnosis and treatment in medical institutions [3]. Hepatitis B virus (HBV) is one of the smallest enveloped DNA viruses that causes acute and chronic infections. HBV is able to evade the immune system of the host and persist lifelong within infected hepatocytes. During active replication, HBV produces enormous viral loads in the blood [4]. Therefore, it is necessary to study the functioning of hepatitis B in liver cell using methods of mathematical and computer modeling. 2. Materials and Methods Mathematical modeling and model analysis of the dynamics of the hepatitis B virus are very important for the study of regulatory mechanisms and the dynamic behavior of the process of viral infection. Many scientific papers have proposed mathematical models describing the dynamics of viral hepatitis B in the liver cell. In these studies, mathematical modeling plays an important role in understanding and quantifying the biological mechanisms that control the dynamics of the hepatitis B virus. Abu O. and Onalo S. E. considered a mathematical model of the dynamics of transmission of the hepatitis B virus, which includes vaccination and treatment as control parameters. With the use of values of model parameters, the properties of the disease-free and the endemic equilibrium were numerically studied [5].