IDEAS home Printed from https://ideas.repec.org/a/hin/complx/4291017.html
   My bibliography  Save this article

A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay

Author

Listed:
  • A. A. M. Arafa
  • M. Khalil
  • A. Sayed

Abstract

The purpose of this paper is to propose a variable fractional-order model with a constant time delay of the coinfection of HIV/AIDS and malaria. The proposed model describes the interaction between HIV/AIDS and malaria. This model is presented by using variable fractional-order derivative which is an extension of the constant fractional-order derivative to explain a certain pattern in the development of infection of several patients. The presented model has been solved numerically via the predictor-corrector scheme. The local and global stability conditions of the disease-free equilibrium are investigated. Also, numerical simulations are presented for different variable fractional-order derivatives in Caputo sense.

Suggested Citation

  • A. A. M. Arafa & M. Khalil & A. Sayed, 2019. "A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay," Complexity, Hindawi, vol. 2019, pages 1-13, March.
    • Handle: RePEc:hin:complx:4291017
    DOI: 10.1155/2019/4291017
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/4291017.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/4291017.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/4291017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    2. Gafiychuk, V. & Datsko, B. & Meleshko, V., 2008. "Analysis of fractional order Bonhoeffer–van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 418-424.
    3. Ricardo Almeida & Agnieszka B. Malinowska & Tatiana Odzijewicz, 2019. "Optimal Leader–Follower Control for the Fractional Opinion Formation Model," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1171-1185, September.
    4. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
    5. Silva, Cristiana J. & Torres, Delfim F.M., 2019. "Stability of a fractional HIV/AIDS model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 180-190.
    6. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    7. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    8. Majumdar, Prahlad & Mondal, Bapin & Debnath, Surajit & Ghosh, Uttam, 2022. "Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    9. Shuai Li & Chengdai Huang & Xinyu Song, 2019. "Bifurcation Based-Delay Feedback Control Strategy for a Fractional-Order Two-Prey One-Predator System," Complexity, Hindawi, vol. 2019, pages 1-13, April.
    10. Al-Mdallal, Qasem M., 2018. "On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 261-267.
    11. Samaneh Soradi Zeid & Mostafa Yousefi, 2016. "A Neural Network Approach for Solving Fractional-Order Model of HIV Infection of CD4+T-Cells," International Journal of Sciences, Office ijSciences, vol. 5(06), pages 65-69, June.
    12. Mohammad Imam Utoyo & Windarto & Aminatus Sa’adah, 2018. "Analysis of Fractional Order Mathematical Model of Hematopoietic Stem Cell Gene-Based Therapy," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-11, August.
    13. Pedjeu, Jean-C. & Ladde, Gangaram S., 2012. "Stochastic fractional differential equations: Modeling, method and analysis," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 279-293.
    14. Rana, Sourav & Bhattacharya, Sabyasachi & Pal, Joydeep & N’Guérékata, Gaston M. & Chattopadhyay, Joydev, 2013. "Paradox of enrichment: A fractional differential approach with memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3610-3621.
    15. Al-khedhairi, A. & Matouk, A.E. & Khan, I., 2019. "Chaotic dynamics and chaos control for the fractional-order geomagnetic field model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 390-401.
    16. Li, Ning & Yan, Mengting, 2022. "Bifurcation control of a delayed fractional-order prey-predator model with cannibalism and disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    17. Matouk, A.E., 2020. "Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    18. Wang, Yupin & Liu, Shutang & Li, Hui & Wang, Da, 2019. "On the spatial Julia set generated by fractional Lotka-Volterra system with noise," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 129-138.
    19. Huo, Jingjing & Zhao, Hongyong, 2016. "Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 41-56.
    20. Hu, Binxin & Song, Qiankun & Zhao, Zhenjiang, 2020. "Robust state estimation for fractional-order complex-valued delayed neural networks with interval parameter uncertainties: LMI approach," Applied Mathematics and Computation, Elsevier, vol. 373(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:4291017. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.