734
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Mathematical modelling with computational fractional order for the unfolding dynamics of the communicable diseases

, , &
Article: 2300330 | Received 03 May 2023, Accepted 21 Dec 2023, Published online: 16 Jan 2024

References

  • Okyere S, Ackora-Prah J. Modeling and analysis of monkeypox disease using fractional derivatives. Results Eng. 2023;17:100786. doi:10.1016/j.rineng.2022.100786
  • ur Rahman M, Alhawael G, Karaca Y. Compartmental analysis of middle eastern respiratory syndrome coronavirus model under fractional operator with next-generation matrix methods. Fractals. 2023.
  • Centers for Disease Control and Prevention 2021 National Center for Emerging and Zoonotic Infectious Diseases(NCEZID), Division of High-Consequence Pathogens and Pathology (DHCPP), Monkeypox, accessed: November 10, 2021.
  • Bunge EM, Hoet B, Chen L, et al. The changing epidemiology of human monkeypox potential threat a systematic review. PLoS Negl Trop Dis. 2022;16(2):e001014. doi:10.1371/journal.pntd.0010141
  • Durski KN, McCollum AM, Nakazawa Y, et al. Emergence of monkeypox West and Central Africa, 1970–2017. Morb Mortal Wkly Rep. 2018;67(10):306–310. doi:10.15585/mmwr.mm6710a5
  • Jezek Z, Szczeniowski M, Paluku K, et al. Human monkeypox: confusion with chickenpox. Acta Trop. 1988;45:297–307.
  • Alakunle E, Moens U, Nchinda G, et al. Monkeypox virus in Nigeria: infection biology, epidemiology, and evolution. Viruses. 2020;12(11):1257. doi:10.3390/v12111257
  • Nguyen PY, Ajisegiri WS, Costantino V, et al. Reemergence of human monkeypox and declining population immunity in the context of urbanization, Nigeria. Emerg Infect Dis. 2021;27:1007.
  • Nigeria Centre for Disease Control, Monkeypox outbreak situation report, accessed: November 10, 2021, 2021.
  • Centers for Disease Control and Prevention, National Center for Emerging and Zoonotic Infectious Diseases (NCEZID), Division of High-Consequence Pathogens and Pathology (DHCPP), Monkeypox, accessed: November 11, 2021, 2021.
  • Guo Q, Li M, Wang C, et al. Host and infectivity prediction of Wuhan 2019 novel coronavirus using deep learning algorithm, BioRxiv, 2020.
  • Peter OJ, Oguntolu FA, Ojo MM, et al. Fractional order mathematical model of monkeypox transmission dynamics. Phys Scr. 2022;97(8):084005. doi:10.1088/1402-4896/ac7ebc
  • Majee S, Jana S, Barman S, et al. Transmission dynamics of monkeypox virus with treatment and vaccination controls: A fractional order mathematical approach. Phys Scr. 2023;98(2):024002. doi:10.1088/1402-4896/acae64
  • Liu P, ur Rahman M, Din A. Fractal fractional based transmission dynamics of COVID-19 epidemic model. Comput Methods Biomech Biomed Engin. 2022;25:1–18.
  • Wang W, Qiao Y, Miao J, et al. Dynamic analysis of fractional-order recurrent neural network with caputo derivative. Int J Bifurc Chaos. 2017;27(12):1750181. doi:10.1142/S0218127417501814
  • Peter OJ, Oguntolu FA, Ojo MM, et al. Fractional order mathematical model of monkeypox transmission dynamics. Phys Scr. 2022;97(8):084005. doi:10.1088/1402-4896/ac7ebc
  • Podlubny I. Fractional differential equations. New York: Academic Press; 1999. (Mathematics in Science and Engineering; Vol. 340).
  • Sar EY, Giresunlu IB. Fractional differential equations. Pramana J Phys. 2016;87:17. doi:10.1007/s12043-016-1225-7
  • Shen WY, Chu YM, ur Rahman M, et al. Mathematical analysis of HBV and HCV co-infection model under nonsingular fractional order derivative. Results Phys. 2021;28:104582. doi:10.1016/j.rinp.2021.104582
  • Zhang L, ur Rahman M, Arfan M, et al. Investigation of mathematical model of transmission co-infection TB in HIV community with a non-singular kernel. Results Phys. 2021;28:104559. doi:10.1016/j.rinp.2021.104559
  • Baleanu D, Jajarmi A, Mohammadi H, et al. A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative. Chaos Solit Fractals. 2020;134:109705. doi:10.1016/j.chaos.2020.109705
  • Defterli O, Baleanu D, Jajarmi A, et al. Fractional treatment: an accelerated mass-spring system. Rom Rep Phys. 2022;74:1–13.
  • Baleanu D, Shekari P, Torkzadeh L, et al. Stability analysis and system properties of Nipah virus transmission: a fractional calculus case study. Chaos Solit Fractals. 2023;166:112990. doi:10.1016/j.chaos.2022.112990
  • Owolabi KM, Pindza E. A nonlinear epidemic model for tuberculosis with Caputo operator and fixed point theory. Healthcare Anal. 2022;2:100111. doi:10.1016/j.health.2022.100111
  • Li B, Zhang T, Zhang C. Investigation of financial bubble mathematical model under fractal–fractional Caputo derivative. FRACTALS (fractals). 2023;31:1–13.
  • Agarwal P, Deniz S, Jain S, et al. A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques. Phys A Stat Mech Appl. 2020;542:122769. doi:10.1016/j.physa.2019.122769
  • Rashid S, Tul Kubra K, Sultana S, et al. An approximate analytical view of physical and biological models in the setting of Caputo operator via Elzaki transform decomposition method. J Comput Appl Math. 2022;413:114378. doi:10.1016/j.cam.2022.114378
  • Chowdhury SMEK, Forkan M, Ahmed SF, et al. Modeling the SARS-CoV-2 parallel transmission dynamics: asymptomatic and symptomatic pathways. Comput Biol Med. 2022;143:105264. doi: 10.1016/j.compbiomed.2022.105264
  • Shams M, Kausar N, Samaniego C, et al. On efficient fractional caputo-Type simultaneous scheme for finding all roots of polynomial equations with biomedical engineering applications. Fractals. 2023;31(04):2340075. doi:10.1142/S0218348X23400753
  • Hassani H, Avazzadeh Z, Tenreiro Machado JA, et al. Optimal solution of a fractional HIV/AIDS epidemic mathematical model. J Comput Biol. 2022;29(3):276–291. doi:10.1089/cmb.2021.0253
  • He Q, Zhang X, Xia P, et al. A comparison research on dynamic characteristics of Chinese and American energy prices. J Glob Inf Manag. 2023;31:1–16.
  • Owolabi KM, Shikongo A. Fractal fractional operator method on HER2+ breast cancer dynamics. Int J Appl Comput Math. 2021;7(3):85. doi:10.1007/s40819-021-01030-5
  • Durur Hülya, Yokuş Aıf, Yavuz M. Behavior analysis and asymptotic stability of the traveling wave solution of the Kaup-Kupershmidt equation for conformable derivative. Fract Calc New Appl Underst Nonlinear Phenom. 2022;3:162.
  • Karaagac B, Owolabi KM, Nisar KS. Analysis and dynamics of illicit drug use described by fractional derivative with Mittag-Leffler kernel. CMC-Comput Mater Cont. 2020;65:1905–1924.
  • Martínez-Farías FJ, Alvarado-Sánchez Aí, Rangel-Cortes E, et al. Bi-dimensional crime model based on anomalous diffusion with law enforcement effect. Math Model Numer Simul Appl. 2022;2:26–40.
  • Naik PA, Zu J, Owolabi KM. Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control. Chaos Solit Fractals. 2020;138:109826. doi:10.1016/j.chaos.2020.109826
  • Li B, Eskandari Z, Avazzadeh Z. Strong resonance bifurcations for a discrete-time prey–predator model. J Appl Math Comput. 2023;69:1–18.
  • Xuan L, ur Rahmamn M, Ahmad S, et al. A new fractional infectious disease model under the non-singular Mittag–Leffler derivative. Waves Random Complex Media. 2022;1–27. doi:10.1080/17455030.2022.2036386.
  • Thabet STM, Abdo MS, Shah K, et al. Study of transmission dynamics of COVID-19 mathematical model under ABC fractional order derivative. Results Phys. 2020;19:103507. doi:10.1016/j.rinp.2020.103507
  • ur Rahman M, Althobaiti A, Riaz MB, et al. A theoretical and numerical study on fractional order biological models with Caputo Fabrizio derivative. Fractal Fract. 2022;6(8):446. doi:10.3390/fractalfract6080446
  • Erturk VS, Godwe E, Baleanu D, et al. Novel fractional-order lagrangian to describe motion of beam on nanowire. Acta Phys Pol A. 2021;140(3):265–272. doi:10.12693/APhysPolA.140.265
  • Liaqat MI, Etemad S, Rezapour S, et al. A novel analytical Aboodh residual power series method for solving linear and nonlinear time-fractional partial differential equations with variable coefficients. AIMS Math. 2022;7(9):16917–16948. doi:10.3934/math.2022929
  • Odibat Z, Baleanu D. Nonlinear dynamics and chaos in fractional differential equations with a new generalized Caputo fractional derivative. Chin J Phys. 2022;77:1003–1014. doi: 10.1016/j.cjph.2021.08.018
  • Abidemi A, Owolabi KM, Pindza E. Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission. Phys A Stat Mech Appl. 2022;597:127259. doi:10.1016/j.physa.2022.127259
  • Yavuz M, Ozköse F, Akman Müzeyyen, et al. A new mathematical model for tuberculosis epidemic under the consciousness effect. Math Model Control. 2023;3(2):88–103. doi:10.3934/mmc.2023009
  • Karaagac B, Owolabi KM. Numerical analysis of polio model: A mathematical approach to epidemiological model using derivative with Mittag–Leffler kernel. Math Methods Appl Sci. 2023;46(7):8175–8192. doi:10.1002/mma.v46.7
  • Gülnur YEL, Kayhan Mç, Ciancio A. A new analytical approach to the (1+ 1)-dimensional conformable fisher equation. Math Model Numer Simul Appl. 2022;2(4):211–220.
  • Naik PA, Owolabi KM, Zu J, et al. Modeling the transmission dynamics of COVID-19 pandemic in Caputo type fractional derivative. J Multiscale Model. 2021;12(3):2150006. doi:10.1142/S1756973721500062
  • Duran S, Durur H, Yavuz M, et al. Discussion of numerical and analytical techniques for the emerging fractional order murnaghan model in materials science. Opt Quantum Electron. 2023;55(6):571. doi:10.1007/s11082-023-04838-1
  • Li B, Eskandari Z, Avazzadeh Z. Dynamical behaviors of an SIR epidemic model with discrete time. Fractal Fract. 2022;6(11):659. doi:10.3390/fractalfract6110659
  • Atangana A, Araz SI. New concept in calculus: piecewise differential and integral operators. Chaos Solit Fractals. 2021;145:110638. doi:10.1016/j.chaos.2020.110638
  • Sohail A, Yu Z, Arif R, et al. Piecewise differentiation of the fractional order CAR-T cells-SARS-2 virus model. Results Phys. 2022;33:105046. doi:10.1016/j.rinp.2021.105046
  • Atangana A, Toufik M. A piecewise heat equation with constant and variable order coefficients: A new approach to capture crossover behaviors in heat diffusion. AIMS Math. 2022;7(5):8374–8389. doi:10.3934/math.2022467
  • Heydari MH, Razzaghi M. A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative. Chaos Solit Fractals. 2021;152:111465. doi:10.1016/j.chaos.2021.111465
  • Shah K, Abdeljawad T, Ali A. Mathematical analysis of the Cauchy type dynamical system under piecewise equations with Caputo fractional derivative. Chaos Solit Fractals. 2022;161:112356. doi:10.1016/j.chaos.2022.112356
  • ur Rahman M, Arfan M, Baleanu D. Piecewise fractional analysis of the migration effect in plant-pathogen-herbivore interactions. Bull Biomath. 2023;1(1):1–23. doi:10.59292/bulletinbiomath.2023001
  • MATLAB, 2022 version 9.12.0 (R2022a). The Math-Works Inc., Natick, Massachusetts.