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Mathematical analysis of an extended SEIR model of COVID-19 using the ABC-fractional operator

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  • Sintunavarat, Wutiphol
  • Turab, Ali

Abstract

This paper aims to suggest a time-fractional SPEPIPAIPSPHPRP model of the COVID-19 pandemic disease in the sense of the Atangana–Baleanu–Caputo operator. The proposed model consists of six compartments: susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized and recovered population. We prove the existence and uniqueness of solutions to the proposed model via fixed point theory. Furthermore, a stability analysis in the context of Ulam–Hyers and the generalized Ulam–Hyers criterion is also discussed. For the approximate solution of the suggested model, we use a well-known and efficient numerical technique, namely the Toufik–Atangana numerical scheme, which validates the importance of arbitrary order derivative ϑ and our obtained theoretical results. Finally, a concise analysis of the simulation is proposed to explain the spread of the infection in society.

Suggested Citation

  • Sintunavarat, Wutiphol & Turab, Ali, 2022. "Mathematical analysis of an extended SEIR model of COVID-19 using the ABC-fractional operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 65-84.
    • Handle: RePEc:eee:matcom:v:198:y:2022:i:c:p:65-84
    DOI: 10.1016/j.matcom.2022.02.009
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    References listed on IDEAS

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    1. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.
    2. Benjamin Ivorra & Beatriz Martínez-López & José Sánchez-Vizcaíno & Ángel Ramos, 2014. "Mathematical formulation and validation of the Be-FAST model for Classical Swine Fever Virus spread between and within farms," Annals of Operations Research, Springer, vol. 219(1), pages 25-47, August.
    3. Badr Alqahtani & Andreea Fulga & Erdal Karapınar, 2018. "Fixed Point Results on Δ-Symmetric Quasi-Metric Space via Simulation Function with an Application to Ulam Stability," Mathematics, MDPI, vol. 6(10), pages 1-19, October.
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    Cited by:

    1. Sergey M. Sitnik & Vladimir E. Fedorov & Nikolay V. Filin & Viktor A. Polunin, 2022. "On the Solvability of Equations with a Distributed Fractional Derivative Given by the Stieltjes Integral," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    2. Silvério Rosa & Delfim F. M. Torres, 2023. "Numerical Fractional Optimal Control of Respiratory Syncytial Virus Infection in Octave/MATLAB," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    3. 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.
    4. Yaping Wang & Lin Hu & Linfei Nie, 2022. "Dynamics of a Hybrid HIV/AIDS Model with Age-Structured, Self-Protection and Media Coverage," Mathematics, MDPI, vol. 11(1), pages 1-27, December.
    5. Azhar Iqbal Kashif Butt & Saira Batool & Muhammad Imran & Muneerah Al Nuwairan, 2023. "Design and Analysis of a New COVID-19 Model with Comparative Study of Control Strategies," Mathematics, MDPI, vol. 11(9), pages 1-29, April.
    6. McSylvester Ejighikeme Omaba & Hamdan Al Sulaimani, 2022. "On Caputo–Katugampola Fractional Stochastic Differential Equation," Mathematics, MDPI, vol. 10(12), pages 1-12, June.
    7. Farai Nyabadza & Josiah Mushanyu & Rachel Mbogo & Gift Muchatibaya, 2023. "Modelling the Influence of Dynamic Social Processes on COVID-19 Infection Dynamics," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    8. Askar Akaev & Alexander I. Zvyagintsev & Askar Sarygulov & Tessaleno Devezas & Andrea Tick & Yuri Ichkitidze, 2022. "Growth Recovery and COVID-19 Pandemic Model: Comparative Analysis for Selected Emerging Economies," Mathematics, MDPI, vol. 10(19), pages 1-18, October.
    9. Siphokazi Princess Gatyeni & Faraimunashe Chirove & Farai Nyabadza, 2022. "Modelling the Potential Impact of Stigma on the Transmission Dynamics of COVID-19 in South Africa," Mathematics, MDPI, vol. 10(18), pages 1-23, September.

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