SpringerLink
Log in

A SIR Epedimic Model Involving Fractional Atangana Derivative

  • Conference paper
  • First Online:
Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization (ICPAMS 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 476))

  • 242 Accesses

Abstract

This paper aime to analyzes a fractional order SIR epidemic model with a nonlinear incidence rate. First, we prove the global existence, positivity and boundedness of the solutions. The stability is studied. Finally, numerical simulations are presented to illustrate our theoretical results.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 192.59
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 246.09
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Abel, N.H.: Solution de quelques problèmes á l’aide d’intégrales définies, Werke 1. Mag. Naturvidenkaberne 10–12 (1823)

    Google Scholar 

  2. Lin, W.: Global existence theory and chaos control of fractional differential equations. J. Math. Anal. Appl. 332, 709–726 (2007)

    Article  MathSciNet  Google Scholar 

  3. Rossikhin, Y.A., Shitikova, M.V.: Application of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl. Mech. Rev. 50, 15–67 (1997)

    Article  Google Scholar 

  4. Jia, G.L., Ming, Y.X.: Study on the viscoelasticity of cancellous bone based on higher-order fractional models. In: Proceeding of the 2nd International Conference on Bioinformatics and Biomedical Engineering (ICBBE 2008), pp. 1733–1736 (2006)

    Google Scholar 

  5. Magin, R.: Fractional calculus in bioengineering. Crit. Rev. Biomed. Eng. 32(1), 13–77 (2004)

    Article  Google Scholar 

  6. Scalas, E., Gorenflo, R., Mainardi, F.: Fractional calculus and continuous-time finance. Phys. A 284(1–4), 376–384 (2000)

    Article  MathSciNet  Google Scholar 

  7. Capponetto, R., Dongola, G., Fortuna, L., Petras, I.: Fractional Order Systems: Modelling and Control Applications. World Scientific Series in Nonlinear Science, Series A, vol. 72 (2010)

    Google Scholar 

  8. Cole, K.S.: Electric conductance of biological systems. In: Cold Spring Harbor Symposia on Quantitative Biology, vol. 1, pp. 107–116 (1933)

    Google Scholar 

  9. Djordjevic, V.D., Jaric, J., Fabry, B., Fredberg, J.J., Stamenovic, D.: Fractional derivatives embody essential features of cell rheological behavior. Ann. Biomed. Eng. 31, 692–699 (2003). https://doi.org/10.1114/1.1574026

    Article  Google Scholar 

  10. Dos Santos, J.P.C., Monteiro, E., Vieira, G.B.: Global stability of fractional SIR epidemic model. Proc. Ser. Braz. Soc. Comput. Appl. Math. 5(1), 1–7 (2017)

    Google Scholar 

  11. Okyere, E., Oduro, F.T., Amponsah, S.K., Dontwi, I.K., Frempong, N.K.: Fractional order SIR model with constant population. Br. J. Math. Comput. Sci. 14(2), 1–12 (2016)

    Article  Google Scholar 

  12. Guo, Y.: The stability of the positive solution for a fractional SIR model. Int. J. Biomath. 10(1), 1–14 (2017)

    Article  MathSciNet  Google Scholar 

  13. Saeedian, M., Khalighi, M., Azimi-Tafreshi, N., Jafari, G.R., Ausloos, M.: Memory effects on epidemic evolution: the susceptible-infected-recovered epidemic model. Phys. Rev. E 95, 022409 (2017)

    Google Scholar 

  14. Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198. Academic Press, San Diego (1998)

    MATH  Google Scholar 

  15. Hattaf, K., Yousfi, N., Tridane, A.: 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 

  16. Boukhouima, A., Hattaf, K., Yousfi, N.: Dynamics of a fractional order HIV infection model with specific functional response and cure rate. Int. J. Differ. Equ. 2017, 8372140 (2017)

    Google Scholar 

  17. Petras, I.: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Springer, Berlin (2011). https://doi.org/10.1007/978-3-642-18101-6

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculté des Sciences et Techniques Béni Mellal, MAROC, Laboratoire de recherche “Mathématiques Appliquées et Calcul Scientifique”, Beni Mellal, Morocco

    H. El-Houari, A. Kraita, L. S. Chadli & H. Moussa

Authors
  1. H. El-Houari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Kraita
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. S. Chadli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Moussa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. S. Chadli .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Sultan Moulay Slimane University, Beni Mellal, Morocco

    Said Melliani

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

El-Houari, H., Kraita, A., Chadli, L.S., Moussa, H. (2023). A SIR Epedimic Model Involving Fractional Atangana Derivative. In: Melliani, S., Castillo, O. (eds) Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization. ICPAMS 2021. Lecture Notes in Networks and Systems, vol 476. Springer, Cham. https://doi.org/10.1007/978-3-031-12416-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-12416-7_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-12415-0

  • Online ISBN: 978-3-031-12416-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation