Analysis of hepatitis B disease with fractal–fractional Caputo derivative using real data from Turkey

Abstract

Scholars and analysts have been increasingly focusing on the concept of modeling contagious illnesses by aid of non-integer order derivatives. It is beyond suspicion that one is able to designate traditional epidemiological models solely via a fixed order, whereas this kind of a fixed order is not associated with the systems in fractional order derivative. In the field of fractional calculus, a newly-instituted fractional calculus has come into play latterly, namely the fractal-fractional operator. This article embraces this new perspective, employing the said operator in a hepatitis B outbreak model, which is one of the prime illnesses to bring about long-term hepatitis, cirrhosis and hepatocellular carcinoma and resulting in high mortality rates every year. First and foremost, we introduced the newly-formulated epidemiological model involving a recently composed operator from the fractal–fractional Caputo category with the fractional order and the fractal dimension. After that, the outcomes obtained from the said fractal–fractional Caputo model was put through an existence-uniqueness analysis. We calculated the disease free and the endemic equilibria and additionally, the reproduction number was detected as R0=1. Over and above these, parameter estimation and fitting are gained for our model utilizing more correctly produced parameters. Several numeric productions of this computer model are submitted herein concerning the said fractal–fractional operator. In this work, we conclude that it is an efficient method to employ numeric arrangements when forecasting and surveying intricate phenomena.