Hepatitis B is a globally infectious disease. It is pretty contagious and can be transmitted by blood or bodily fluids, through things like sharing razors and toothbrushes. It has been called the silent killer because it is asymptomatic, one might have the virus but not know until it manifests itself until much later. Since people do not give attention, it will develop into cirrhosis and hepatocellular carcinoma that leads to liver transplantation and death. This nature of HBV disease motivated us to perform this work. Mathematical modeling of HBV transmission is an interesting research area. In this paper, we present characteristics of HBV virus transmission in the form of a mathematical model. We proposed and analyzed a compartmental nonlinear deterministic mathematical model SEACTR for transmission dynamics and control of hepatitis B virus disease. In this model, we used force infection which takes the contact rate of susceptible population and transmission probability into account. We proved that the solution of the considered dynamical system is positive and bounded. The model is studied qualitatively using the stability theory of differential equations and the effective reproductive number which represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The sensitivity index shows that the transfer rate from exposed class to acute infective class and transfer rate from exposed class to chronic infective class are the most dominant parameters contributing to the transmission of HBV. On the one hand, the vaccination rate and treatment rate are the parameters that suppress the transmission of the disease the most, and enhancing the vaccination rate for newborns and treatment for chronically infected individuals is very effective to stop the transmission of HBV. The combined efforts of vaccination, effective treatment, and interruption of transmission make elimination of the infection plausible and may eventually lead to the eradication of the virus.
Background: Because of its asymptomatic nature, the Hepatitis B Virus (HBV) has become the most lethal and silent killer. In this research, we offer HBV virus transmission characteristics in the form of a mathematical model. We suggested and examined a seven-compartment compartmental nonlinear deterministic mathematical model for transmission dynamics with immigration and HBV reactivation after recovery, as well as control measures for Hepatitis B virus disease transmission. By considering the following facts and cases, this work will provide new knowledge. First, re-infection of HBV after liver transplantation, chemotherapy, and other therapies is one of the most essential aspects in HBV transmission, although reactivation of HBV was not taken into account in some compartmental models of HBV transmission. Furthermore, the exposure rate, immigration rate, and level of infectiousness of the chronic infective class were not given enough weight in the numerical assessment of the force of HBV infection. These facts influenced the development of our model. Methods: We demonstrated that the solution of the dynamical system under consideration is positive and bounded. The effective reproductive number that represents the epidemic indicator is generated from the biggest eigenvalue of the netgeneration matrix, and the model is examined qualitatively using differential equation stability theory. For disease-free and endemic equilibria, both local and global asymptotic stability criteria are determined. Results: A full explanation of the parameters and their numerical findings is presented and debated well based on the numerical simulation. Conclusions: According to the findings of this study, vaccination and treatment interventions play a critical role in reducing HBV transmission and reproduction. It has also been demonstrated that HBV reactivation contributes significantly to an increase in theinfective population, which boosts virus transmission, and that a combination of vaccination and treatment will be the most effective strategy for controlling HBV infection and reinfection after recovery.
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