DOI: https://doi.org/10.14710/jfma.v6i1.17174

FRACTIONAL MATHEMATICAL MODEL OF HIV AND CD4+ T-CELLS INTERACTIONS WITH HAART TREATMENT

*Muhammad Rifki Nisardi orcid  -  Department of Actuarial Science, Univesitas Muhammadiyah Bulukumba, Jl Poros Bulukumba - Bantaeng, Km. 9, Kabupaten Bulukumba, Indonesia., Indonesia
Kasbawati Kasbawati  -  Department of Mathematics, Universitas Hasanuddin Makassar, Indonesia
Restu Ananda Putra  -  Department of Mathematics, Universitas Gajah Mada Yogyakarta, Indonesia

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Abstract

This study provides the mathematical model of the interaction between the HIV and CD4+ T cells. This research develops other research by formulating a model with the fractional Caputo derivative approach with fractional order α. Based on the model, we obtain the equilibrium point and analyze the stability criterion of the equilibrium point. Furthermore, we perform the Next Generation Matrix method to calculate the basic reproduction number. Then, we apply the Grunwald-Letnikov Explicit method to show the numerical result of the model.

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Keywords: : HIV-Model; Fractional Order; Basic Reproduction Number; Grunwald-Letnikov Method.

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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  1. Maimunah and D. Aldila, “Mathematical model for HIV spreads control program with ART treatment,” in Journal of Physics: Conference Series, Mar. 2018, vol. 974, no. 1. doi: 10.1088/1742-6596/974/1/012035
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  3. S. Cassels, S. J. Clark, and M. Morris, “Mathematical Models for HIV Transmission Dynamics: Tools for Social and Behavioral Science Research NIH Public Access,” J Acquir Immune Defic Syndr, vol. 47, no. 1, pp. 34–39, 2008, doi: 10.1097/QAI
  4. Attaullah and M. Sohaib, “Mathematical modeling and numerical simulation of HIV infection model,” Results in Applied Mathematics, vol. 7, Aug. 2020, doi: 10.1016/j.rinam.2020.100118
  5. L. Wang and M. Y. Li, “Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells,” Math Biosci, vol. 200, no. 1, pp. 44–57, Mar. 2006, doi: 10.1016/j.mbs.2005.12.026
  6. T. K. Ayele, E. F. Doungmo Goufo, and S. Mugisha, “Mathematical modeling of HIV/AIDS with optimal control: A case study in Ethiopia,” Results Phys, vol. 26, Jul. 2021, doi: 10.1016/j.rinp.2021.104263
  7. S. Kumar, R. Kumar, J. Singh, K. S. Nisar, and D. Kumar, “An efficient numerical scheme for fractional model of HIV-1 infection of CD4+ T-cells with the effect of antiviral drug therapy,” Alexandria Engineering Journal, vol. 59, no. 4, pp. 2053–2064, Aug. 2020, doi: 10.1016/j.aej.2019.12.046
  8. Fatmawati, M. A. Khan, and H. P. Odinsyah, “Fractional model of HIV transmission with awareness effect,” Chaos Solitons Fractals, vol. 138, Sep. 2020, doi: 10.1016/j.chaos.2020.109967
  9. M. R. Nisardi, K. Kasbawati, K. Khaeruddin, A. Robinet, and K. Chetehouna, “Fractional Mathematical Model of Covid-19 with Quarantine,” InPrime: Indonesian Journal of Pure and Applied Mathematics, vol. 4, no. 1, pp. 33–48, Apr. 2022, doi: 10.15408/inprime.v4i1.23719
  10. H. Khan, F. Ahmad, O. Tunç, and M. Idrees, “On fractal-fractional Covid-19 mathematical model,” Chaos Solitons Fractals, vol. 157, Apr. 2022, doi: 10.1016/j.chaos.2022.111937
  11. Y. Belgaid, M. Helal, A. Lakmeche, and E. Venturino, “A mathematical study of a coronavirus model with the caputo fractional-order derivative,” Fractal and Fractional, vol. 5, no. 3, Sep. 2021, doi: 10.3390/fractalfract5030087
  12. T. Cui, P. Liu, and A. Din, “Fractal–fractional and stochastic analysis of norovirus transmission epidemic model with vaccination effects,” Sci Rep, vol. 11, no. 1, Dec. 2021, doi: 10.1038/s41598-021-03732-8
  13. S. Rashid, M. K. Iqbal, A. M. Alshehri, R. Ashraf, and F. Jarad, “A comprehensive analysis of the stochastic fractal–fractional tuberculosis model via Mittag-Leffler kernel and white noise,” Results Phys, vol. 39, p. 105764, Aug. 2022, doi: 10.1016/j.rinp.2022.105764
  14. F. Ndairou, I. Area, J. Nieto, C. Silva, and D. F. M. Torres, “Fractional model of COVID-19 applied to Galicia, Spain and Portugal,” Chaos Solitons Fractals, vol. 144, p. 110652, Jan. 2021, doi: 10.1016/j.chaos.2021.110652
  15. N. Ozalp and E. Demirci, “A fractional order SEIR model with vertical transmission,” Math Comput Model, vol. 54, pp. 1–6, Jan. 2011, doi: 10.1016/j.mcm.2010.12.051
  16. S. Suriani, S. Toaha, and K. Kasbawati, “MSEICR Fractional Order Mathematical Model of The Spread Hepatitis B,” Jurnal Matematika, Statistika dan Komputasi, vol. 17, pp. 314–324, Dec. 2020, doi: 10.20956/jmsk.v17i2.10994
  17. S. Boulaaras, R. Jan, A. Khan, and M. Ahsan, “Dynamical analysis of the transmission of dengue fever via Caputo-Fabrizio fractional derivative R,” 2022, doi: 10.1016/j.csfx.2022.10
  18. S. S. Askar, D. Ghosh, P. K. Santra, A. A. Elsadany, and G. S. Mahapatra, “A fractional order SITR mathematical model for forecasting of transmission of COVID-19 of India with lockdown effect,” Results Phys, vol. 24, May 2021, doi: 10.1016/j.rinp.2021.104067
  19. I. Podlubny, “Chapter 2 - Fractional Derivatives and Integrals,” in Fractional Differential Equations, vol. 198, I. Podlubny, Ed. Elsevier, 1999, pp. 41–119. doi: https://doi.org/10.1016/S0076-5392(99)80021-6
  20. I. Petráš, “Fractional-Order Systems,” in Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Berlin, Heidelberg: Springer Berlin Heidelberg, 2011, pp. 43–54. doi: 10.1007/978-3-642-18101-6_3
  21. M. Tavazoei and M. Haeri, “A necessary condition for double scroll attractor existence in fractional-order systems,” Phys Lett A, vol. 367, pp. 102–113, Jan. 2007, doi: 10.1016/j.physleta.2007.05.081
  22. D. Matignon, “Stability Results For Fractional Differential Equations With Applications To Control Processing,” vol. 2, Jan. 1997
  23. N. ’Izzati Hamdan and A. Kilicman, “A fractional order SIR epidemic model for dengue transmission,” Chaos, Solitons and Fractals, vol. 114. Jan. 2018. doi: 10.1016/j.chaos.2018.06.031
  24. E. Ahmed, A. El-Sayed, and H. El-Saka, “On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rössler, Chua and Chen systems,” Phys Lett A, vol. 358, pp. 1–4, Jan. 2006, doi: 10.1016/j.physleta.2006.04.087
  25. N. Chitnis, J. Hyman, and J. Cushing, “Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model,” Bull Math Biol, vol. 70, pp. 1272–1296, Jan. 2008, doi: 10.1007/s11538-008-9299-0
  26. R. Scherer, S. Kalla, Y. Tang, and J. Huang, “The Grnwald-Letnikov method for fractional differential equations,” Computers & Mathematics with Applications, vol. 62, pp. 902–917, Jan. 2011, doi: 10.1016/j.camwa.2011.03.054
  27. L. Carvalho De Barros et al., “The Memory Effect on Fractional Calculus: An Application in the Spread of Covid-19.”
  28. I. Dzhalladova and M. Růžičková, “Stability of The Equilibrium of Nonlinear Dynamical Systems,” Tatra Mountains Mathematical Publications, vol. 71, pp. 71–80, Jan. 2018, doi: 10.2478/tmmp-2018-0007

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