A new fractional model for the dynamics of the hepatitis B virus using the Caputo-Fabrizio derivative
Department of Mathematics, University of Peshawar, Peshawar, KP, Pakistan
2 Department of Mathematics, City University of Science and Information Technology, Peshawar, KP, Pakistan
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Accepted: 15 May 2018
Published online: 26 June 2018
Hepatitis B is the major public health issue of the entire world. In mathematical epidemiology, mathematical models play a vital role in understanding the dynamics of infectious diseases. Therefore, in the present paper, we formulate a mathematical model for the hepatitis B virus with the Caputo-Fabrizio fractional derivative with non-singular kernel. Initially, we discuss some basic results involved in the model and then apply the fractional calculus to the proposed model to describe the hepatitis B virus with an arbitrary-order derivative having non-singular kernel. An iterative method is proposed for the solution of the model. For the model variables existence, we use the fixed-point theorem. Further, the uniqueness of the solution is verified. Graphical results are obtained for different values of the fractional parameter.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018