IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v116y2018icp268-277.html
   My bibliography  Save this article

A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives

Author

Listed:
  • Aliyu, Aliyu Isa
  • Inc, Mustafa
  • Yusuf, Abdullahi
  • Baleanu, Dumitru

Abstract

The model of transmission dynamics of vector-borne diseases with vertical transmission and cure within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced. The effect of vertical transmission and cure rate on the basic reproduction number is shown. The Atangana–Baleanu fractional operator in caputo sense (ABC) with non-singular and non-local kernels is used to study the model. The existence and uniqueness of solutions are investigated using the Picard–Lindel method. Ultimately, for illustrating the acquired results, we perform some numerical simulations and show graphically to observe the impact of the arbitrary order derivative. It is expected that the proposed model will show better approximation than the classical model established before.

Suggested Citation

  • Aliyu, Aliyu Isa & Inc, Mustafa & Yusuf, Abdullahi & Baleanu, Dumitru, 2018. "A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 268-277.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:268-277
    DOI: 10.1016/j.chaos.2018.09.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918306623
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.09.043?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
    2. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 520-531.
    3. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    4. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Asamoah, Joshua Kiddy K. & Fatmawati,, 2023. "A fractional mathematical model of heartwater transmission dynamics considering nymph and adult amblyomma ticks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Korpinar, Zeliha & Inc, Mustafa & Bayram, Mustafa, 2020. "Theory and application for the system of fractional Burger equations with Mittag leffler kernel," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    3. Djaoue, Seraphin & Guilsou Kolaye, Gabriel & Abboubakar, Hamadjam & Abba Ari, Ado Adamou & Damakoa, Irepran, 2020. "Mathematical modeling, analysis and numerical simulation of the COVID-19 transmission with mitigation of control strategies used in Cameroon," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Qureshi, Sania & Aziz, Shaheen, 2020. "Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    5. Kumar, Sunil & Chauhan, R.P. & Momani, Shaher & Hadid, Samir, 2021. "A study of fractional TB model due to mycobacterium tuberculosis bacteria," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    6. Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    7. Fatmawati, & Khan, Muhammad Altaf & Azizah, Muftiyatul & Windarto, & Ullah, Saif, 2019. "A fractional model for the dynamics of competition between commercial and rural banks in Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 32-46.

    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. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    2. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.
    3. Taneco-Hernández, M.A. & Morales-Delgado, V.F. & Gómez-Aguilar, J.F., 2019. "Fundamental solutions of the fractional Fresnel equation in the real half-line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 807-827.
    4. Khan, Hasib & Gómez-Aguilar, J.F. & Khan, Aziz & Khan, Tahir Saeed, 2019. "Stability analysis for fractional order advection–reaction diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 737-751.
    5. Saad, Khaled M. & Srivastava, H.M. & Gómez-Aguilar, J.F., 2020. "A Fractional Quadratic autocatalysis associated with chemical clock reactions involving linear inhibition," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    6. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    7. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    8. Bonyah, Ebenezer & Gómez-Aguilar, J.F. & Adu, Augustina, 2018. "Stability analysis and optimal control of a fractional human African trypanosomiasis model," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 150-160.
    9. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.
    10. Owolabi, Kolade M., 2019. "Mathematical modelling and analysis of love dynamics: A fractional approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 849-865.
    11. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.
    12. Owolabi, Kolade M. & Hammouch, Zakia, 2019. "Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1072-1090.
    13. Saad, Khaled M. & Gómez-Aguilar, J.F. & Almadiy, Abdulrhman A., 2020. "A fractional numerical study on a chronic hepatitis C virus infection model with immune response," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    14. Singh, Harendra & Srivastava, H.M., 2019. "Jacobi collocation method for the approximate solution of some fractional-order Riccati differential equations with variable coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1130-1149.
    15. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    16. Abdeljawad, Thabet & Atangana, Abdon & Gómez-Aguilar, J.F. & Jarad, Fahd, 2019. "On a more general fractional integration by parts formulae and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    17. Prakash, Amit & Kaur, Hardish, 2019. "Analysis and numerical simulation of fractional order Cahn–Allen model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 134-142.
    18. Hashemi, M.S. & Inc, Mustafa & Yusuf, Abdullahi, 2020. "On three-dimensional variable order time fractional chaotic system with nonsingular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    19. Korpinar, Zeliha & Inc, Mustafa & Bayram, Mustafa, 2020. "Theory and application for the system of fractional Burger equations with Mittag leffler kernel," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    20. Ávalos-Ruiz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2018. "FPGA implementation and control of chaotic systems involving the variable-order fractional operator with Mittag–Leffler law," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 177-189.

    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:eee:chsofr:v:116:y:2018:i:c:p:268-277. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.