Modeling of hepatitis B epidemic model with fractional operator

Abstract

AbstractIn many regions across the world, hepatitis B virus (HBV) infection is still endemic and the transmission rate is much greater than majority of the known epidemic diseases. Numerous mathematical models (utilizing various differential operators) have been put forth over the past 20 years to understand the transmission mechanism of HBV in various nations and geographical areas. In this manuscript, an epidemic model with various novelties for capturing the dynamic of HBV while utilizing Caputo–Fabrizio fractional differential operator with asymptomatic carriers and vaccination effects is introduced. Initially, the model is formulated by using the ordinary derivative, and afterward, the fractional differential operator is applied to transform the model into arbitrary-ordered derivative. A few basic mathematical properties for the proposed integer-ordered model is presented. The existence of solution to the problem and its uniqueness of the fractional order model are established by transforming the problem into integral equations and then applying the standard results of fixed point theory. For boundedness and positivity of model’ solution is elaborated utilizing the techniques of fractional calculus. It is too much important to validate the theoretical findings through simulations; therefore, the solution curves of the model under consideration are displayed by using the well-known approach called the Mittag-Leffler. To show the behavior of the order of the operator on the dynamics of the disease, various graphical illustrations are presented at the end of the manuscript. By comparing the findings of the present study with the available literature, it is observed that fractional derivative is better to use than integer-order operator for capturing the realistic scenario of the disease.