Asymptotic analysis of hepatitis B epidemic model using Caputo Fabrizio fractional operator

Abstract

AbstractA mathematical model representing the temporal dynamics of hepatitis B virus (HBV) is discussed in this research work. This is based on the asymptomatic carriers and symptomatic individuals keeping in view the characteristics of the disease. We also incorporate the vaccination parameter to vaccinate susceptible individuals. Moreover, we use fractional calculus to extend the model to its associated fractional-order. For this, we particularly use the fractional operator of the Caputo-Fabrizio type to fractionalize the proposed model. First, the model formulation has been derived in classic order and then extended to its associated fractional-order version for generalization. The model equilibria was calculated, and the basic reproductive number was found. Then we will discuss the existence with properties of the uniqueness of the proposed fractional version of the model that is under consideration. The positivity with boundedness is shown to investigate that the considered model is feasible biologically as well as mathematically. Finally, we use the Mittag–Leffler approach to visualize the model of fractional-order and to support the results carried out in the theocratical part. We also demonstrate the solution curves for different values of the fractional parameter to differentiate between integer-order and fractional-order on the disease transmission.