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Fractional order mathematical modeling of COVID-19 transmission

Author

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  • Ahmad, Shabir
  • Ullah, Aman
  • Al-Mdallal, Qasem M.
  • Khan, Hasib
  • Shah, Kamal
  • Khan, Aziz

Abstract

In this article, the mathematical model with different compartments for the transmission dynamics of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding the existence of at least one solution through fixed point results are derived. Then for the concerned approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is utilized. Initially, we simulate the results by using some available data for different fractional-order to show the appropriateness of the proposed method. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

Suggested Citation

  • Ahmad, Shabir & Ullah, Aman & Al-Mdallal, Qasem M. & Khan, Hasib & Shah, Kamal & Khan, Aziz, 2020. "Fractional order mathematical modeling of COVID-19 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920306524
    DOI: 10.1016/j.chaos.2020.110256
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    References listed on IDEAS

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    1. Fazal Haq & Muhammad Shahzad & Shakoor Muhammad & Hafiz Abdul Wahab & Ghaus ur Rahman, 2017. "Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-7, December.
    2. Jajarmi, Amin & Yusuf, Abdullahi & Baleanu, Dumitru & Inc, Mustafa, 2020. "A new fractional HRSV model and its optimal control: A non-singular operator approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    3. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Torres, Delfim F.M., 2020. "Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    4. Rihan, F.A. & Al-Mdallal, Q.M. & AlSakaji, H.J. & Hashish, A., 2019. "A fractional-order epidemic model with time-delay and nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 97-105.
    5. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    6. Abdo, Mohammed S. & Shah, Kamal & Wahash, Hanan A. & Panchal, Satish K., 2020. "On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
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    Cited by:

    1. Khatun, Mst Sebi & Das, Samhita & Das, Pritha, 2023. "Dynamics and control of an SITR COVID-19 model with awareness and hospital bed dependency," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Alexander Domoshnitsky & Alexander Sitkin & Lea Zuckerman, 2022. "Mathematical Modeling of COVID-19 Transmission in the Form of System of Integro-Differential Equations," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    3. Arshad, Sadia & Siddique, Imran & Nawaz, Fariha & Shaheen, Aqila & Khurshid, Hina, 2023. "Dynamics of a fractional order mathematical model for COVID-19 epidemic transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    4. Maurício de Carvalho, João P.S. & Moreira-Pinto, Beatriz, 2021. "A fractional-order model for CoViD-19 dynamics with reinfection and the importance of quarantine," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    5. Asif, Muhammad & Ali Khan, Zar & Haider, Nadeem & Al-Mdallal, Qasem, 2020. "Numerical simulation for solution of SEIR models by meshless and finite difference methods," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    6. Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Alotaibi, Naif D., 2021. "A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    7. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. Ullah, Mohammad Sharif & Higazy, M. & Kabir, K.M. Ariful, 2022. "Dynamic analysis of mean-field and fractional-order epidemic vaccination strategies by evolutionary game approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    9. Koutou, Ousmane & Diabaté, Abou Bakari & Sangaré, Boureima, 2023. "Mathematical analysis of the impact of the media coverage in mitigating the outbreak of COVID-19," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 600-618.
    10. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    11. Liu, Yang & Chen, Liping & Wu, Xiaobo & Lopes, António M. & Cui, Fengqi & Chen, YangQuan, 2023. "Theoretical analysis and experimental verification of fractional-order RC cobweb circuit network," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    12. Amar Nath Chatterjee & Fahad Al Basir & Bashir Ahmad & Ahmed Alsaedi, 2022. "A Fractional-Order Compartmental Model of Vaccination for COVID-19 with the Fear Factor," Mathematics, MDPI, vol. 10(9), pages 1-15, April.
    13. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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