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During acute hepatitis B virus infection viral loads reach dangerous peaks, virtually every hepatocyte becomes infected with a disease-B virus virus. Here, we review results from a group of people who were acutely HBV infection and develop mathematical models to determine the role of immune responses in different stages of early HBV infection. We are able to distinguish the kinetics of the noncytolytic and the cytolytic immune responses from the patient's data, revealing the relative involvement of these two processes. We also learned that newly produced uninfected cells are resistant to viral infection, which can result in productivity decline. ".
"Fractional differential equations are starting to gain more traction in modeling physical and biological processes. " In several situations, it is worth mentioning that the commonly used mathematical representations of integer-order derivatives, including nonlinear models, do not provide a complete framework. Using the Atangana-Baleanu fractional derivative, a mathematical model for COVID-19 and Hepatitis B Virus co-interaction is developed and tested in this work. The disease-free and endemic equilibria are found to be globally asymptotically stable under certain circumstances, thanks to carefully constructed Lyapunov functions. The modeling's behavior is discussed using a fixed point theory. The effect of the fractional derivative on the final model is also highlighted. The findings in this paper show that HBV and COVID-19 transmission rates can significantly influence the rates of both disease co-infection.
"This paper presents a comprehensive review of a stochastic delayed model that governs the transmission mechanism of the Hepatitis B virus, while considering both white noises and vaccination effects. The disturbances are nonlinear, and an individual may lose his/her immunity after the vaccination, implying that the vaccination can cause temporal immunity. The model was then extended to a stochastic framework, and it has been shown that the model solution exists globally, bounded stochastically, and is positive. We fitted the model against the available HBV data in Pakistan from March 2018 to February 2019, and accordingly the model's parameters were estimated. ".
In this research study, "In this research study, a mathematical model representing the temporal dynamics of hepatitis B virus is discussed. " In addition, we use fractional calculus to extend the model to its appropriate fractional-order. We will address the existence of the proposed fractional version of the model that is under discussion with the uniqueness of the model. We will not worry about the existence with attributes of the model's uniqueness. The positivity with boundedness is shown to show that the proposed scheme is both economically and mathematically attainable. We also displayed the solution curves for various values of the fractional parameter to help distinguish between integer-order and fractional-order disease transmission. ".
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