The analysis of fractional-order hepatitis B epidemiological model

Abstract

We study the epidemiology of hepatitis B for different infection routes with hospitalization keeping in view the aesthetic concept to model it with the fractional calculus application. We will use the Caputo–Fabrizio operator for the purposes of fractionation and discuss the existence analyses with uniqueness properties for the newly formulated model. We apply the fixed-point theorem to prove the analysis of existence with uniqueness. It also proves that the model has positive solutions and abounded solutions. We also calculate the reproductive number to discuss steady states, and to perform that the particular epidemic model is stable asymptotically under some constraints. Particularly, we will discuss both the global and local properties of the proposed model by using the mean value theorem, Barbalat's lemma and linearization. We also draw some numerical simulations to verify the theoretical work via some graphical representations.