Modeling and analysis of Hepatitis B dynamics with vaccination and treatment with novel fractional derivative.

These days, fractional calculus is essential for studying the dynamic transmission of illnesses, developing control systems, and solving several other real-world issues. In this study, we develop a Hepatitis B (HBV) model to observe the dynamics of vaccination and treatment effects to control the disease by using novel fractional operator. Modified Atangana-Baleanu-Caputo (MABC) is a new definition of the used derivative that is based on a modification of the Atangana and Baleanu derivatives. By employing the MABC fractional derivative, which incorporates the concepts of non-locality and memory effects our model captures the complex dynamics of HBV transmission more accurately than traditional models. An objective of this study is to analyze the effect of immunization and treatment techniques on the course of the hepatitis B virus, with a particular focus on the changing order of differentiation. Thereby, our paper deals with the stability analysis, positiveness, existence and uniqueness of the solution and simulations. Analysis of reproductive number R0 with the impact of different parameters is also treated. The proposed model's existence and uniqueness findings are examined through the use of Banach's fixed point and Leray-Schauder nonlinear alternative theorems. The equilibria for the models are determined to be globally stable using Lyapunov functions. The simulations for certain parameters are achieved by applying the Lagrange interpolation for the numerical computations and also the results are compared with the ABC operator results. The model is validated using numerical simulations, which are also used to assess how well different intervention techniques work to lower the impact of HBV infection and prevent its spread throughout the community. The results of this research assist in developing public health policies intended to lower the incidence of HBV infection worldwide and offer insightful information about how well treatment and vaccination strategies work to prevent HBV disease.