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A new fractional model for the dynamics of the hepatitis B virus using the Caputo-Fabrizio derivative

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Abstract.

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, KP, Pakistan

    Saif Ullah & Muhammad Farooq

  2. Department of Mathematics, City University of Science and Information Technology, Peshawar, KP, Pakistan

    Muhammad Altaf Khan

Authors
  1. Saif Ullah
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  2. Muhammad Altaf Khan
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  3. Muhammad Farooq
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Correspondence to Muhammad Altaf Khan.

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Ullah, S., Altaf Khan, M. & Farooq, M. A new fractional model for the dynamics of the hepatitis B virus using the Caputo-Fabrizio derivative. Eur. Phys. J. Plus 133, 237 (2018). https://doi.org/10.1140/epjp/i2018-12072-4

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  • DOI: https://doi.org/10.1140/epjp/i2018-12072-4

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