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Fractional model of HIV transmission with awareness effect

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  • 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
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    References listed on IDEAS

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    1. 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.
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    3. 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.
    4. 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.
    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.
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    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.

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