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Babakordi, Fatemeh, Allahviranloo, Tofigh. (1403). Application of fuzzy ABC fractional differential equations in infectious diseases. سامانه مدیریت نشریات علمی, 12(1), 1-15. doi: 10.22034/cmde.2023.47768.2000
Fatemeh Babakordi; Tofigh Allahviranloo. "Application of fuzzy ABC fractional differential equations in infectious diseases". سامانه مدیریت نشریات علمی, 12, 1, 1403, 1-15. doi: 10.22034/cmde.2023.47768.2000
Babakordi, Fatemeh, Allahviranloo, Tofigh. (1403). 'Application of fuzzy ABC fractional differential equations in infectious diseases', سامانه مدیریت نشریات علمی, 12(1), pp. 1-15. doi: 10.22034/cmde.2023.47768.2000
Babakordi, Fatemeh, Allahviranloo, Tofigh. Application of fuzzy ABC fractional differential equations in infectious diseases. سامانه مدیریت نشریات علمی, 1403; 12(1): 1-15. doi: 10.22034/cmde.2023.47768.2000

Application of fuzzy ABC fractional differential equations in infectious diseases

Computational Methods for Differential Equations
مقاله 1، دوره 12، شماره 1، فروردین 2024، صفحه 1-15    اصل مقاله (567.74 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.47768.2000
نویسندگان
Fatemeh Babakordi* 1؛ Tofigh Allahviranloo2، 3
1Department of Mathematics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran.
2Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Tukey.
3Department of mathematics, Science and research branch, Islamic Azad university, Tehran, Iran.
چکیده
In this paper, for solving the HIV fuzzy mathematical model, it is first transformed into a system of three nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with three unknowns and fuzzy initial values. Then, using the generalized Hukuhara difference and ABC fractional derivative and applying the fuzzy numerical ABC-PI method, its fuzzy solution is calculated. Moreover, some theorems are defined to prove the existence and uniqueness of the solution. Then, it is explained that the proposed method can In this paper, for solving the HIV fuzzy mathematical model, it is first transformed into a system of three nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with three unknowns and fuzzy initial values. Then, using the generalized Hukuhara difference and ABC fractional derivative and applying the fuzzy numerical ABC-PI method, its fuzzy solution is calculated. Moreover, some theorems are defined to prove the existence and uniqueness of the solution. Then, it is explained that the proposed method can be used for the system of any  equations with  unknowns.  Therefore, in order to determine the solution of the fuzzy mathematical model of the transmission of COVID-19, it is transformed into a system of six nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with six unknowns and fuzzy initial values and is solved similarly. At the end, a numerical example is presented to verify the effectiveness of the proposed method.be used for the system of any equations with unknowns. Therefore, in order to determine the solution of the fuzzy mathematical model of the transmission of COVID-19, it is transformed into a system of six nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with six unknowns and fuzzy initial values and is solved similarly. At the end, a numerical example is presented to verify the effectiveness of the proposed method.
کلیدواژه‌ها
Fuzzy Atangana-Baleanu-Caputo(ABC) fractional derivative؛ Fuzzy ABC fractional differential equations؛ HIV fuzzy mathematical model
مراجع
  • [1] S. Ahmad, A. Ullah, K. Shah, S. Salahshour, A. Ahmadian, and T. Ciano, Fuzzy fractional-order model of the novel coronavirus, Advances in Difference Equation, 2020.
  • [2] T. Allahviranloo and B. Ghanbari, On the fuzzy fractional differential equation with interval Atangana-Baleanu fractional derivative approach, Chaos, Solitons and Fractals, 130 (2020), 109397.
  • [3] D. Aldila, Mathematical model for HIV spreads control program with ART treatment, Journal of Physics, Confer- ence Series, 974(1) (2018).
  • [4] A. Arafa, SZ. Rida, and M. Khalil, Fractional modeling dynamics of HIV and CD4+ t-cells during primary infection, Nonlinear Biomed Phys 6(1) (2012), 7.
  • [5] A. Armand, T. Allahviranloo, S. Abbasbandy, and Z. Gouyandeh, The fuzzy generalized Taylor’s expansion with application in fractional differential equations, Iranian Journal of Fuzzy Systems, 16(2) (2019), 57–72.
  • [6] M. Asaduzzaman Chowdhury, Q. ZShah, M. Abul Kashem, A. Shahid, and N. Akhtar, Evaluation of the Effect of Environmental Parameters on the Spread of COVID-19: A Fuzzy Logic Approach, Advances in Fuzzy Systems, 2020, 8829227.
  • [7] W. Assawinchaichote, Control of HIV/AIDS infection system with drug dosages design via robust H fuzzy controller, Bio-medical materials and engineering, 26(1) (2015), S1945–S1951.
  • [8] D. Baleanu, H. Mohammadi, and S. Rezapour, A fractional differential equation model for the COVID-19 trans- mission by using the Caputo–Fabrizio derivative, Advances in Difference Equation, 2020.
  • [9] D. Baleanu, H. Mohammadi, and S. Rezapour, A fractional differential equation model for the COVID-19 trans- mission by using the Caputo–Fabrizio derivative, Advances in Difference Equations, 2020, 299.
  • [10] B. Bede and L. Stefanini, Solution of fuzzy differential equations with generalized differentiabillity using LU parametric representation, EUSFLAT, 2011, 785–790.
  • [11] L. Basnarkov, SEAIR epidemic spreading model of COVID-19, Chaos, Solitons & Fractals 2020, 110394.
  • [12] S. Boccaletti, W. Ditto, G. Mindlin, and A. Atangana, Modeling and forecasting of epidemic spreading: The case of COVID-19 and beyond, Chaos, Solitons & Fractals, 135 (2020), 109794.
  • [13] S. B. Chen, F. Rajaee, A. Yousefpour, R. Alcaraz, Y. M. Chu, J. F. G´omez-Aguilar, S. Bekiros, A. A. Aly, and H. Jahanshahi, Antiretroviral therapy of HIV infection using a novel optimal type-2 fuzzy control strategy, Alexandria Engineering Journal, 60(1) (2021), 1545–1555.
  • [14] S. Djilali and B. Ghanbari, Coronavirus pandemic: A predictive analysis of the peak outbreak epidemic in South Africa, Turkey, and Brazil, Chaos, Solitons & Fractals, 138 (2020), 109971.
  • [15] C. Henry and Y. Frederic, On the behavior of solutions in viral dynamical models, BioSystems, 73 (2004), 157–161.
  • [16] M. A. Khan and A. Atangana, Modeling the dynamics of novel coronavirus (2019-ncov) with fractional derivative, Alex. Eng. J., 2020.
  • [17] H. Kheiri and M. Jafari, Stability analysis of a fractional order model for the HIV/AIDS epidemic in a patchy environment, J. Comput. Appl. Math., 346 (2019), 323–339.
  • [18] R. Lu, X. Zhao, J. Li, P. Niu, B. Yang, H. Wu, and W. Tan, Genomic characterisation and epidemiology of 2019 novel coronavirus: implications for virus origins and receptor binding, Lancet, 6736(20) (2020), 1–10.
  • [19] J. E. Mac´ıas-D´ıaz, Nonlinear wave transmission in harmonically driven Hamiltonian sine-Gordon regimes with memory effects, Chaos, Solitons & Fractals, 2020, 110362.
  • [20] R. May and R. Anderson, Transmission dynamics of HIV infection, Nature., 326 (1987), 137–42.
  • [21] A. Mohammed, A. Al-qaness, A. E. Ahmed, F. Hong, and A.A. Mohamed, Optimization Method for Forecasting Confirmed Cases of COVID-19 in China, Journal of clinical medicine, 2020, 674.
  • [22] B. Narasimhamurthy and K. Leelavathy, Mathematical model approach to HIV/AIDS transmission from mother to child, IJSTR., 1(9) 2012), 52–61.
  • [23] G. Nazir, K. Shah, A. Debbouche, and R. Ali Khan, Study of HIV mathematical model under nonsingular kernel type derivative of fractional order, Chaos, Solitons and Fractals 139 (2020), 110095.
  • [24] A. Perelson, A. Neumann, M. Markowitz, J. Leonard, and D. Ho, HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Science, 271(1582) (1996).
  • [25] C. Pinto, A. Carvalho, D. Baleanu, and H. Srivastava, Efficacy of the post-expo- sure prophylaxis and of the HIV latent reservoir in HIV infection, Mathematics, 7(515) (2019).
  • [26] L. Rong, M. Gilchrist, Z. Feng, and A. Perelson, Modeling within host HIV-1 dynamics and the evolution of drug resistance: tradeoffs between viral enzyme function and drug susceptibility, J Theor Biol, 247 (2007), 804–18.
  • [27] M. J. Rosana, Fuzzy Modeling in Symptomatic HIV Virus Infected Population, Bulletin of Mathematical Biology, 66 (2004), 1597–1620.
  • [28] M. J. Rosana, C. B. La'ecio, and C. B. Rodney, A Fuzzy Delay Differential Equation Model for HIV Dynamics, Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July, 2009, 20–24.
  • [29] H. Shim, S. J. Han, C. C. Chung, S. W. Nam, and J. H. Seo, Optimal scheduling of drug treatment for HIV infection: continuous dose control and receding horizon control, Int. J. Control Autom. Syst., 1 (2003), 282–288.
  • [30] L. Stefanini and B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differ- ential equations, Nonlinear Analysis, 71(3-4) (2009), 1311–1328.
  • [31] K. Yao, H. Chen, W. H. Peng, Z. Wang, J. Yao, and W. peng, A new method on Box dimension of Weyl-Marchaud fractional derivative of Weierstrass function, Chaos, Solitons & Fractals, 2020, 110317.
  • [32] H. Zarei, A. Vahidian Kamyad, and A. A. Heydari, Fuzzy Modeling and Control of HIV Infection, Computational and Mathematical Methods in Medicine, 2012, Article ID 893474, 17 pages.
  • [33] P. Zhou, X. L. Yang, X. G. Wang, B. Hu, L. Zhang, W. Zhang, Z. L. Shi, H. R. Si, Y. Zhu, B. Li, and C. L. Huang, A pneumonia outbreak associated with a new coronavirus of probable bat origin, Nature, 579(7798) (2020), 270–273.
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