Affiliation:
1. Department of Mathematics, Chandigarh University, Mohali 140413, India
Abstract
In this paper, we delve into the analysis of the Hepatitis B model, specifically the [Formula: see text] model, within the scope of the Caputo–Fabrizio fractional operator. A new state variable the number of vaccinated individuals is also added to the model. This addition enriches the scope of the hepatitis B model inviting a deeper exploration of the subject matter. Our study proves the existence of a disease-free fixed point within the proposed compartmental model. To ensure the existence and uniqueness of the fixed point, we employ a fixed-point result in the b-complete b-dislocated quasi-metric space, utilizing a Geraghty-type contraction mapping. This approach establishes the fixed point of a disease-free state within the model. Furthermore, we employ a two-step Adams–Bashforth numerical scheme, serving as a validation of both the significance of fractional-order derivatives and the validity of our obtained theoretical results. Together our research presents an innovative perspective on the [Formula: see text] hepatitis B model pushing the boundaries of understanding and shedding light on the dynamics of disease transmission with the impact of vaccine.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Computational Theory and Mathematics,Computer Science Applications,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics