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A mathematical study on a fractional COVID-19 transmission model within the framework of nonsingular and nonlocal kernel

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  • Okposo, Newton I.
  • Adewole, Matthew O.
  • Okposo, Emamuzo N.
  • Ojarikre, Herietta I.
  • Abdullah, Farah A.

Abstract

In this work, a mathematical model consisting of a compartmentalized coupled nonlinear system of fractional order differential equations describing the transmission dynamics of COVID-19 is studied. The fractional derivative is taken in the Atangana-Baleanu-Caputo sense. The basic dynamic properties of the fractional model such as invariant region, existence of equilibrium points as well as basic reproduction number are briefly discussed. Qualitative results on the existence and uniqueness of solutions via a fixed point argument as well as stability of the model solutions in the sense of Ulam-Hyers are furnished. Furthermore, the model is fitted to the COVID-19 data circulated by Nigeria Centre for Disease Control and the two-step Adams-Bashforth method incorporating the noninteger order parameter is used to obtain an iterative scheme from which numerical results for the model can be generated. Numerical simulations for the proposed model using Adams-Bashforth iterative scheme are presented to describe the behaviors at distinct values of the fractional index parameter for of each of the system state variables. It was shown numerically that the value of fractional index parameter has a significant effect on the transmission behavior of the disease however, the infected population (the exposed, the asymptomatic infectious, the symptomatic infectious) shrinks with time when the basic reproduction number is less than one irrespective of the value of fractional index parameter.

Suggested Citation

  • Okposo, Newton I. & Adewole, Matthew O. & Okposo, Emamuzo N. & Ojarikre, Herietta I. & Abdullah, Farah A., 2021. "A mathematical study on a fractional COVID-19 transmission model within the framework of nonsingular and nonlocal kernel," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007815
    DOI: 10.1016/j.chaos.2021.111427
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    References listed on IDEAS

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    1. Bozkurt, Fatma & Yousef, Ali & Baleanu, Dumitru & Alzabut, Jehad, 2020. "A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Gao, Wei & Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D. G. & Kumar, Pushpendra, 2020. "A new study of unreported cases of 2019-nCOV epidemic outbreaks," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Okuonghae, D. & Omame, A., 2020. "Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Baba, Isa Abdullahi & Nasidi, Bashir Ahmad, 2021. "Fractional Order Model for the Role of Mild Cases in the Transmission of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Saad, Khaled M. & Gómez-Aguilar, J.F. & Almadiy, Abdulrhman A., 2020. "A fractional numerical study on a chronic hepatitis C virus infection model with immune response," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Verma, Pratibha & Kumar, Manoj, 2021. "Analysis of a novel coronavirus (2019-nCOV) system with variable Caputo-Fabrizio fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Peng Zhou & Hang Fan & Tian Lan & Xing-Lou Yang & Wei-Feng Shi & Wei Zhang & Yan Zhu & Ya-Wei Zhang & Qing-Mei Xie & Shailendra Mani & Xiao-Shuang Zheng & Bei Li & Jin-Man Li & Hua Guo & Guang-Qian Pe, 2018. "Fatal swine acute diarrhoea syndrome caused by an HKU2-related coronavirus of bat origin," Nature, Nature, vol. 556(7700), pages 255-258, April.
    8. 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.
    9. Khan, Aziz & Gómez-Aguilar, J.F. & Saeed Khan, Tahir & Khan, Hasib, 2019. "Stability analysis and numerical solutions of fractional order HIV/AIDS model," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 119-128.
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    1. Antonios Kalampakas & Sovan Samanta & Jayanta Bera & Kinkar Chandra Das, 2024. "A Fuzzy Logic Inference Model for the Evaluation of the Effect of Extrinsic Factors on the Transmission of Infectious Diseases," Mathematics, MDPI, vol. 12(5), pages 1-18, February.
    2. Prem Kumar, R. & Santra, P.K. & Mahapatra, G.S., 2023. "Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 741-766.

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