IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v138y2020ics0960077920303660.html
   My bibliography  Save this article

Fractional model of HIV transmission with awareness effect

Author

Listed:
  • Fatmawati,
  • Khan, Muhammad Altaf
  • Odinsyah, Hafidz Putra

Abstract

In this work, we study the HIV dynamics with fractional operator of Caputo type. We use the real data of HIV infection cases of Indonesia from 2006 to 2018 and parameterized the HIV model and estimate the basic reproduction number is R0≈2.2763. First, we give brief mathematical formulation of HIV/AIDS population in integer order derivative. Then, we present some background results related to the model. The integer model is then generalized by using the Caputo derivative and present the mathematical results that associated to the model. We use novel technique for the solution of fractional mathematical model of HIV using Newton polynomial approach and obtain the numerical solution graphically. The data fitting versus model for fractional order p is shown which shows that the model give better result than the integer order. Some graphical for the important parameter were shown. The model is shown locally asymptotically when R0 less or greater than 1.

Suggested Citation

  • Fatmawati, & Khan, Muhammad Altaf & Odinsyah, Hafidz Putra, 2020. "Fractional model of HIV transmission with awareness effect," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303660
    DOI: 10.1016/j.chaos.2020.109967
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920303660
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109967?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. Fatmawati & Endrik Mifta Shaiful & Mohammad Imam Utoyo, 2018. "A Fractional-Order Model for HIV Dynamics in a Two-Sex Population," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-11, April.
    2. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    3. Atangana, Abdon & Bouallegue, Ghaith & Bouallegue, Kais, 2020. "New multi-scroll attractors obtained via Julia set mapping," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. 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.
    5. 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.
    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. 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).
    2. Kar, Silajit & Maiti, Dilip K. & Maiti, Atasi Patra, 2024. "Impacts of non-locality and memory kernel of fractional derivative, awareness and treatment strategies on HIV/AIDS prevalence," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    3. Zhai, Xuanpei & Li, Wenshuang & Wei, Fengying & Mao, Xuerong, 2023. "Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Baleanu, Dumitru & Hasanabadi, Manijeh & Mahmoudzadeh Vaziri, Asadollah & Jajarmi, Amin, 2023. "A new intervention strategy for an HIV/AIDS transmission by a general fractional modeling and an optimal control approach," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    5. Yaping Wang & Lin Hu & Linfei Nie, 2022. "Dynamics of a Hybrid HIV/AIDS Model with Age-Structured, Self-Protection and Media Coverage," Mathematics, MDPI, vol. 11(1), pages 1-27, December.

    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. Chukwu, C.W. & Fatmawati, & Utoyo, M.I. & Setiawan, A. & Akanni, J.O., 2024. "Fractional model of HIV transmission on workplace productivity using real data from Indonesia," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 1089-1103.
    2. Wang, Wanting & Khan, Muhammad Altaf & Fatmawati, & Kumam, P. & Thounthong, P., 2019. "A comparison study of bank data in fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 369-384.
    3. Goyal, Manish & Baskonus, Haci Mehmet & Prakash, Amit, 2020. "Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Cheng, Guanghui & Li, Dan & Yao, Yuangen & Gui, Rong, 2023. "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Hao, Wenhui & Zhang, Juping & Jin, Zhen, 2024. "Dynamic analysis and optimal control of HIV/AIDS model with ideological transfer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 578-605.
    7. Asamoah, Joshua Kiddy K. & Okyere, Eric & Yankson, Ernest & Opoku, Alex Akwasi & Adom-Konadu, Agnes & Acheampong, Edward & Arthur, Yarhands Dissou, 2022. "Non-fractional and fractional mathematical analysis and simulations for Q fever," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Mishra, A.M. & Purohit, S.D. & Owolabi, K.M. & Sharma, Y.D., 2020. "A nonlinear epidemiological model considering asymptotic and quarantine classes for SARS CoV-2 virus," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    9. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2021. "A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    11. 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.
    12. Kolebaje, Olusola & Popoola, Oyebola & Khan, Muhammad Altaf & Oyewande, Oluwole, 2020. "An epidemiological approach to insurgent population modeling with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    13. Li, Zhongfei & Liu, Zhuang & Khan, Muhammad Altaf, 2020. "Fractional investigation of bank data with fractal-fractional Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    14. Maike A. F. dos Santos, 2019. "Mittag–Leffler Memory Kernel in Lévy Flights," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    15. Erman, Sertaç & Demir, Ali, 2020. "On the construction and stability analysis of the solution of linear fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    16. Yousefpour, Amin & Jahanshahi, Hadi & Bekiros, Stelios, 2020. "Optimal policies for control of the novel coronavirus disease (COVID-19) outbreak," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    17. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    18. Aneefah H. S. Alenazy & Abdelhalim Ebaid & Ebrahem A. Algehyne & Hind K. Al-Jeaid, 2022. "Advanced Study on the Delay Differential Equation y ′( t ) = ay ( t ) + by ( ct )," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
    19. Yadav, Ram Prasad & Renu Verma,, 2020. "A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    20. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

    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:138:y:2020:i:c:s0960077920303660. 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.