170
Views
0
CrossRef citations to date
0
Altmetric
Research Article

A fractional-order generalized Richards growth model and its implementation to COVID-19 data

ORCID Icon, ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 345-357 | Received 22 Feb 2024, Accepted 29 May 2024, Published online: 24 Jun 2024

References

  • Abdeljawad, T., Al-Mdallal, Q. M., & Jarad, F. (2019). Fractional logistic models in the frame of fractional operators generated by conformable derivatives. Chaos, Solitons & Fractals, 119, 94–101. doi:10.1016/j.chaos.2018.12.015
  • Abdeljawad, T., Hajji, M. A., Al-Mdallal, Q. M., & Jarad, F. (2020). Analysis of some generalized ABC–fractional logistic models. Alexandria Engineering Journal, 59(4), 2141–2148. doi:10.1016/j.aej.2020.01.030
  • Ali, A., Ur Rahmamn, M., Shah, Z., Kumam, P., & Adnan. (2022). Investigation of a time-fractional covid-19 mathematical model with singular kernel. Advances in Continuous and Discrete models, 2022(1), 34. doi:10.1186/s13662-022-03701-z
  • Alrabaiah, H., Arfan, M., Shah, K., Mahariq, I., & Ullah, A. (2021). A comparative study of spreading of novel corona virus disease by using fractional order modified SEIR model. Alexandria Engineering Journal, 60(1), 573–585. doi:10.1016/j.aej.2020.09.036
  • Atangana, A., & Baleanu, D. (2016). New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. Thermal Science, 20(2), 763–769. doi:10.2298/TSCI160111018A
  • Ausloos, M. (2006). The logistic map and the route to chaos: From the beginnings to modern applications. Berlin: Springer Science & Business Media.
  • Baleanu, D., Jajarmi, A., & Hajipour, M. (2018). On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel. Nonlinear Dynamics, 94(1), 397–414. doi:10.1007/s11071-018-4367-y
  • Bürger, R., Chowell, G., & Lara-Díaz, L. Y. (2021). Measuring differences between phenomenological growth models applied to epidemiology. Mathematical Biosciences, 334, 108558. doi:10.1016/j.mbs.2021.108558
  • Chowell, G. (2017). Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts. Infectious Disease Modelling, 2(3), 379–398. doi:10.1016/j.idm.2017.08.001
  • Chowell, G., & Viboud, C. (2016). Is it growing exponentially fast?–Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics. Infectious Disease Modelling, 1(1), 71–78. doi:10.1016/j.idm.2016.07.004
  • Darti, I., Habibah, U., Astutik, S., Kusumawinahyu, W. M., & Suryanto, A. (2021). Comparison of phenomenological growth models in predicting cumulative number of COVID-19 cases in East Java Province, Indonesia. Communications in Mathematical Biology and Neuroscience, 2021, 14.
  • Darti, I., Musafir, R. R., Rayungsari, M., Suryanto, A., & Trisilowati. (2023). Dynamics of a fractional-order covid-19 epidemic model with quarantine and standard incidence rate. Axioms, 12(6), 591. doi:10.3390/axioms12060591
  • Darti, I., Suryanto, A., Panigoro, H. S., & Susanto, H. (2021). Forecasting covid-19 epidemic in Spain and Italy using a generalized Richards model with quantified uncertainty. Communication in Biomathematical Sciences, 3(2), 90–100. doi:10.5614/cbms.2020.3.2.1
  • Diethelm, K. (2010). The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type. Berlin: Springer Science & Business Media.
  • Diethelm, K., Ford, N. J., & Freed, A. D. (2002). A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics, 29(1/4), 3–22. doi:10.1023/A:1016592219341
  • Djeddi, N., Hasan, S., Al-Smadi, M., & Momani, S. (2020). Modified analytical approach for generalized quadratic and cubic logistic models with Caputo-Fabrizio fractional derivative. Alexandria Engineering Journal, 59(6), 5111–5122. doi:10.1016/j.aej.2020.09.041
  • Du, M., Wang, Z., & Hu, H. (2013). Measuring memory with the order of fractional derivative. Scientific Reports, 3(1), 3431. doi:10.1038/srep03431
  • Ezz-Eldien, S. (2018). On solving fractional logistic population models with applications. Computational and Applied Mathematics, 37(5), 6392–6409. doi:10.1007/s40314-018-0693-4
  • Haidong, Q., Ur Rahman, M., Al Hazmi, S. E., Yassen, M. F., Salahshour, S., Salimi, M., & Ahmadian, A. (2023). Analysis of non-equilibrium 4d dynamical system with fractal fractional Mittag–Leffler kernel. Engineering Science and Technology, an International Journal, 37, 101319. doi:10.1016/j.jestch.2022.101319
  • Jaelani, A, Fatmawati, F., & Fitri, N. D. Y. (2021). Stability analysis and optimal control of mathematical epidemic model with medical treatment. AIP Conference Proceedings, (vol. 2329, pp. 040001). AIP Publishing.
  • Jafari, H., Ganji, R., Nkomo, N., & Lv, Y. (2021). A numerical study of fractional order population dynamics model. Results in Physics, 27, 104456. doi:10.1016/j.rinp.2021.104456
  • Khan, Z. A., Shah, K., Abdalla, B., & Abdeljawad, T. (2023). A numerical study of complex dynamics of a Chemostat model under fractal-fractional derivative. Fractals, 31(08), 2340181. doi:10.1142/S0218348X23401813
  • Li, B., Zhang, T., & Zhang, C. (2023). Investigation of financial bubble mathematical model under fractal-fractional Caputo derivative. Fractals, 31(05), 1–13. doi:10.1142/S0218348X23500500
  • Miller, K. S., & Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. New York: Willy.
  • Musafir, R. R., Suryanto, A., Darti, I. & Trisilowat. (2024a). Comparison of fractional-order monkeypox model with singular and non-singular kernels. Jambura Journal of Biomathematics, 5(1)
  • Musafir, R. R., Suryanto, A., Darti, I., & Trisilowati. (2024b). Optimal control of a fractional-order monkeypox epidemic model with vaccination and rodents culling. Results in Control and Optimization, 14, 100381. doi:10.1016/j.rico.2024.100381
  • Musafir, R. R., Suryanto, A., Darti, I., & Trisilowati. (2024c). Stability analysis of a fractional-order monkeypox epidemic model with quarantine and hospitalization. Journal of Biosafety and Biosecurity, 6(1), 34–50. doi:10.1016/j.jobb.2024.02.003
  • Panigoro, H. S., Suryanto, A., Kusumawinahyu, W. M., & Darti, I. (2021). Dynamics of an eco-epidemic predator-prey model involving fractional derivatives with power-law and Mittag–Leffler kernel. Symmetry, 13(5), 785. doi:10.3390/sym13050785
  • Pincheira-Brown, P., & Bentancor, A. (2021). Forecasting covid-19 infections with the semi-unrestricted generalized growth model. Epidemics, 37, 100486. doi:10.1016/j.epidem.2021.100486
  • Podlubny, I. (1999). Fractional differential equations: Mathematics in science and engineering. San Diego: Academic Press.
  • Rahman, M., Tabassum, S., Althobaiti, A., Althobaiti, S., & Waseem. (2024). An analysis of fractional piecewise derivative models of dengue transmission using deep neural network. Journal of Taibah University for Science, 18(1), 2340871. doi:10.1080/16583655.2024.2340871
  • Rahmi, E., Darti, I., Suryanto, A., & Trisilowati, (2021). A modified Leslie–Gower model incorporating Beddington–Deangelis functional response, double Allee effect and memory effect. Fractal and Fractional, 5(3), 84. doi:10.3390/fractalfract5030084
  • Richards, F. J. (1959). A flexible growth function for empirical use. Journal of Experimental Botany, 10(2), 290–301. doi:10.1093/jxb/10.2.290
  • Roosa, K., Lee, Y., Luo, R., Kirpich, A., Rothenberg, R., Hyman, J. M., & Chowell, G. (2020). Short-term forecasts of the covid-19 epidemic in Guangdong and Zhejiang, China. Journal of Clinical Mmedicine, 9(2), 596. February 13–23, 2020
  • Shah, K., & Abdeljawad, T. (2023). On complex fractal-fractional order mathematical modeling of co 2 emanations from energy sector. Physica Scripta, 99(1), 015226. doi:10.1088/1402-4896/ad1286
  • Shah, K., Abdalla, B., Abdeljawad, T., & Alqudah, M. A. (2024). A fractal-fractional order model to study multiple sclerosis: A chronic disease. Fractals, 32(02), 2440010. doi:10.1142/S0218348X24400103
  • Shah, K., Ahmad, I., Mukheimer, A., Abdeljawad, T., Jeelani, M. B., & Shafiullah. (2024). On the existence and numerical simulation of cholera epidemic model. Open Physics, 22(1), 20230165. doi:10.1515/phys-2023-0165
  • Trisilowati, Darti, I., Musafir, R. R., Rayungsari, M., & Suryanto, A., & Trisilowati. (2023). Dynamics of a fractional-order covid-19 epidemic model with quarantine and standard incidence rate. Axioms, 12(6), 591. doi:10.3390/axioms12060591
  • Ullah, M. S., Kabir, K. A., & Khan, M. A. H. (2023). A non-singular fractional-order logistic growth model with multi-scaling effects to analyze and forecast population growth in Bangladesh. Scientific Reports, 13(1), 20118. doi:10.1038/s41598-023-45773-1
  • Viboud, C., Simonsen, L., & Chowell, G. (2016). A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks. Epidemics, 15, 27–37. doi:10.1016/j.epidem.2016.01.002
  • Wu, K., Darcet, D., Wang, Q., & Sornette, D. (2020). Generalized logistic growth modeling of the covid-19 outbreak: Comparing the dynamics in the 29 provinces in china and in the rest of the world. Nonlinear Dynamics, 101(3), 1561–1581. doi:10.1007/s11071-020-05862-6
  • Zhang, L., Rahman, M. U., Ahmad, S., Riaz, M. B., & Jarad, F. (2022). Dynamics of fractional order delay model of coronavirus disease. AIMS Mathematics, 7(3), 4211–4232. doi:10.3934/math.2022234