Skip to main content

A Fractional Order Model for HBV Infection with Capsids and Cure Rate

  • Chapter
  • First Online:

Abstract

In this work, we propose and analyze a fractional order model for hepatitis B virus (HBV) infection with capsids and cure of infected cells. We first prove the existence, positivity, and boundedness of solutions in order to ensure the well-posedness of our proposed model. By constructing appropriate Lyapunov functionals, the global stability of the steady states is established. Numerical simulations are presented in order to validate our theoretical results.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. WHO, Hepatitis B (2017). http://www.who.int/news-room/fact-sheets/detail/hepatitis-b

  2. X. Zhou, Q. Sun, Stability analysis of a fractional-order HBV infection model. Int. J. Adv. Appl. Math. Mech. 2(2), 1–6 (2014)

    MathSciNet  MATH  Google Scholar 

  3. S.M. Salman, A.M. Yousef, On a fractional-order model for HBV infection with cure of infected cells. J. Egypt. Math. Soc. 25, 445–451 (2017)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. L.G. Guidotti, R. Rochford, J. Chung, M. Shapiro, R. Purcell, F.V. Chisari, Viral clearance without destruction of infected cells during acute HBV infection. Science 284(5415), 825–829 (1999)

    Article  Google Scholar 

  6. S.R. Lewin, R.M. Ribeiro, T. Walters, G.K. Lau, S. Bowden, S. Locarnini, A.S. Perelson, Analysis of hepatitis B viral load decline under potent therapy: complex decay profiles observed. Hepatology 34, 101–1020 (2001)

    Article  Google Scholar 

  7. K. Hattaf, N. Yousfi, Hepatitis B virus infection model with logistic hepatocyte growth and cure rate. Appl. Math. Sci. 5, 2327–2335 (2011)

    MathSciNet  MATH  Google Scholar 

  8. K. Hattaf, N. Yousfi, A class of delayed viral infection models with general incidence rate and adaptive immune response. Int. J. Dynam. Control 4, 254–265 (2016)

    Article  MathSciNet  Google Scholar 

  9. M. Mahrouf, E.M. Lotfi, M. Maziane, K. Hattaf, N. Yousfi, A stochastic viral infection model with general functional response. Nonlinear Anal. Differ. Equ. 4, 435–445 (2016)

    Article  Google Scholar 

  10. D. Riad, K. Hattaf, N. Yousfi, Dynamics of capital-labour model with Hattaf-Yousfi functional response. Br. J. Math. Comput. Sci. 18(5), 1–7 (2016)

    Article  Google Scholar 

  11. K. Hattaf, N. Yousfi, A. Tridane, Stability analysis of a virus dynamics model with general incidence rate and two delays. Appl. Math. Comput. 221, 514–521 (2013)

    MathSciNet  MATH  Google Scholar 

  12. K. Manna, S.P. Chakrabarty, Chronic hepatitis B infection and HBV DNA-containing capsids: modeling and analysis. Commun. Nonlinear Sci. Numer. Simul. 22, 383–395 (2015)

    Article  MathSciNet  Google Scholar 

  13. K. Manna, Global properties of a HBV infection model with HBV DNA-containing capsids and CTL immune response. Int. J. Appl. Comput. Math. 3(3), 2323–2338 (2017)

    Article  MathSciNet  Google Scholar 

  14. A. Boukhouima, K. Hattaf, N. Yousfi, Dynamics of a fractional order HIV infection model with specific functional response and cure rate. Int. J. Differ. Equ. 2017, 1–8 (2017)

    Article  MathSciNet  Google Scholar 

  15. C.V. De-Leon, Volterra-type Lyapunov functions for fractional-order epidemic systems. Commun. Nonlinear Sci. Numer. Simul. 24, 75–85 (2015)

    Article  MathSciNet  Google Scholar 

  16. J. Huo, H. Zhao, L. Zhu, The effect of vaccines on backward bifurcation in a fractional order HIV model. Nonlinear Anal. Real World Appl. 26, 289–305 (2015)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bachraou, M., Hattaf, K., Yousfi, N. (2019). A Fractional Order Model for HBV Infection with Capsids and Cure Rate. In: Mondaini, R. (eds) Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-23433-1_23

Download citation

Publish with us

Policies and ethics