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Analysis of fractional-order models for hepatitis B

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Abstract

This paper presents two models for hepatitis B, both given by fractional differential equations. The first model is formulated without parameters that indicate drug therapy, while the second one considers the drug therapy. The basic reproduction number and the stability analysis are considered for both models. Moreover, some numerical simulations by nonstandard finite difference schemes are presented. The numerical results show that the solutions converges to an equilibrium point as predicted in the stability analysis.

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Notes

  1. Note that, from Definition 2, that \(I^\alpha t^\beta =t^{\beta +\alpha }\Gamma (\beta +1)/\Gamma (\beta +\alpha +1),\) i.e., the polynomial case is a recovered if \(\alpha ,\beta \in \mathbb {N}\).

  2. This fact is one of the main differences between the fractional derivatives of Camargo and de Oliveira (2015).

  3. As made in Driessche and Watmough (2002) the basic reproduction number will be the biggest eigenvalue of K. For convenience, we omit the square root.

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Acknowledgements

LCC thanks CAPES, and RFC thanks CNPq (universal 455920-2014-1) for financial support. The authors thanks the research group CF@FC for the important and productive discussion.

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Authors and Affiliations

  1. Depto de Bioestatística, UNESP, Botucatu, Brazil

    L. C. Cardoso & F. L. P. Dos Santos

  2. Depto de Ciências, UNESP, Bauru, Brazil

    R. F. Camargo

Authors
  1. L. C. Cardoso
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  2. F. L. P. Dos Santos
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  3. R. F. Camargo
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Corresponding author

Correspondence to R. F. Camargo.

Additional information

Communicated by José Tenreiro Machado.

L. C. Cardoso is supported by NSF Grant CAPES - 1515153.

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Cardoso, L.C., Dos Santos, F.L.P. & Camargo, R.F. Analysis of fractional-order models for hepatitis B. Comp. Appl. Math. 37, 4570–4586 (2018). https://doi.org/10.1007/s40314-018-0588-4

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  • DOI: https://doi.org/10.1007/s40314-018-0588-4

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