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Non-singular kernel-based time-fractional order Covid-19 mathematical model with vaccination

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Abstract

Recently, numerous demonstrative investigations on the mathematical modelling and analysis of Covid-19 have been performed. In this regard, a mathematical model is introduced to demonstrate the effects of vaccination on Covid-19. This study presents the five compartmental groups of the model, namely susceptible, infected, exposed, recovered groups, and vaccinated people. To make the model more realistic, the existing integer-order system has been modified using the Mittag–Leffler kernel. The formation of a fractional-order model shows the validity of this generalization with memory. In addition to the positivity solution, existence, uniqueness, and biologically feasible region are considered. The Ulam–Hyers stability is established through fixed-point theory and nonlinear analysis. The basic reproduction number, which means the number of people predicted to be secondarily infected among the susceptible population, is calculated. The considered model is assessed by using the Atangana–Baleanu fractional operator, and the fractional Adams–Bashforth numerical technique based on Lagrange polynomial interpolation is adopted to solve the model. Further, the error analysis of the present method has also been included. The behaviour of the solution is demonstrated through numerical simulations with the help of graphical representations.

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References

  1. World Health Organization Weakly Report, https://www.who.int/publications/m/item/weekly-epidemiological-update---5-january-2021

  2. World Health Organization. https://covid19.who.int

  3. J Zu, M L Li, Z F Li, M W Shen, Y N Xiao and F P Ji, Infectious Diseases of Poverty 9, 1 (2020)

    Article  Google Scholar 

  4. B Tang, F Xia, S Tang, N L Bragazzi, Q Li, X Sun, J Liang, Y Xiao and J Wu, Int. J. Infectious Diseases 96, 636 (2020)

    Article  Google Scholar 

  5. A Ahmed, B Salam, M Mohammad, A Akgul and S H A Khoshnaw, AIMS Bioengineering 7, 130 (2020)

    Article  Google Scholar 

  6. D Okuonghae and A Omame, Chaos, Solitons and Fractals 139, 110032 (2020)

    Article  MathSciNet  Google Scholar 

  7. B H Foy, B Wahl, K Mehta, A Shet, G I Menon and C Britto, Int. J. Infectious Diseases 103, 431 (2020)

    Article  Google Scholar 

  8. J Farooq and M A Bazaz, Chaos, Solitons and Fractals 138, 110148 (2020)

    Article  MathSciNet  Google Scholar 

  9. C Xu, M Farman, A Hasan, A Akgül, M Zakarya, W Albalawi and C Parkg, Alexandria Engineering J. 61(12), 11787 (2022)

    Article  Google Scholar 

  10. A Akgül, N Ahmed, A Raza, Z Iqbal, M Rafiq, D Baleanu and M A Rehman, Results in Phys. 20, 103663 (2021)

    Article  Google Scholar 

  11. R M Jena, S Chakraverty and S K Jena, Chaos, Solitons & Fractals 141, 1 (2020)

    Article  Google Scholar 

  12. R M Jena, S Chakraverty and D Baleanu, Math.Computers in Simulation 182, 514 (2020)

    Article  Google Scholar 

  13. S Chakraverty, R M Jena and S K Jena, Synthesis Lectures on Mathematics and Statistics, Morgan & Claypool Publishers (2020)

  14. R M Jena, S Chakraverty, M Yavuz and T Abdeljawad, Mod. Phys. Lett. B 35(30), 2150443 (2021)

    Article  ADS  Google Scholar 

  15. S P Kaur and V Gupta, Virus Res. 288, 198114 (2020)

    Article  Google Scholar 

  16. M Yavuz, F Ö Coşar, F Günay and F N Özdemir, Open J. Modelling and Simulation 9, 299 (2021)

    Article  Google Scholar 

  17. M Caputo and M Fabrizio, Prog. Fract. Differ. Appl. 1, 73 (2015)

    Google Scholar 

  18. V F Morales-Delgado, J F Gómez-Aguilar and M A Taneco-Hernandez, Int. J. Electron. Commun. 85, 61 (2018)

    Article  Google Scholar 

  19. Z Li, Z Liu and M A Khan, Chaos Solitons Fractals 131, 109528 (2020)

    Article  MathSciNet  Google Scholar 

  20. S Qureshi and A Atangana, Chaos Solitons Fractals 136, 109812 (2020)

    Article  MathSciNet  Google Scholar 

  21. R Ali, A Akgül and M I Asjad, Pramana – J. Phys. 94, 131 (2020)

    Article  ADS  Google Scholar 

  22. M N Khan, I Ahmad, A Akgül, H Ahmad and P Thounthong, Pramana – J. Phys. 95, 6 (2021)

    Article  ADS  Google Scholar 

  23. L N Huynh, N H Luc, D Baleanu and L D Long, J. Inequal. Appl. 2021, 28 (2021)

    Article  Google Scholar 

  24. P Sunthrayuth, A Alderremy, S Aly, R Shah and A Akgül, Pramana – J. Phys. 95, 201 (2021)

    Article  ADS  Google Scholar 

  25. A Atangana and D Baleanu, Therm. Sci. 20, 1 (2016)

    Article  Google Scholar 

  26. A Atangana and S I Araz, Alex. Eng. J. 59(4), 2355 (2020)

    Article  Google Scholar 

  27. A Atangana and S I Araz, Adv. Differ. Equ. 2021, 57 (2021)

    Article  Google Scholar 

  28. A Atangana, Alex. Eng. J. 60(4), 3781 (2021)

    Article  Google Scholar 

  29. A Atangana and S I Araz, Adv. Differ. Equ. 2020, 659 (2020)

    Article  Google Scholar 

  30. M. Farman, A Akgül, M U Saleem, S Imtiaz and A Ahmad, Pramana – J. Phys. 94, 164 (2020)

    Article  ADS  Google Scholar 

  31. J Kongson, W Sudsutad, C Thaiprayoon, J Alzabut and C Tearnbucha, Adv. Difference Equations 2021, 356 (2021)

    Article  Google Scholar 

  32. M Mandal, S Jana, S K Nandi, A Khatua, S Adak and T K Ka, Chaos, Solitons and Fractals 136, 109889 (2020)

    Article  MathSciNet  Google Scholar 

  33. Z M Odibat and N T Shawagfeh, Appl. Math. Comput. 186(1), 286 (2007)

    Article  MathSciNet  Google Scholar 

  34. X Q Zhao, Dynamical Systems in Population Biology, Springer, Cham (2017) 285 pages

  35. C Castillo-Chavez, Z Feng and W Huang, Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, Springer, Berlin (2002) vol. 125

  36. Z Ali, A Zada and K Shah, Bull. Malays. Math. Sci. Soc. 42(5), 2681 (2019)

    Article  MathSciNet  Google Scholar 

  37. M S Abdo, S K Panchal, K Shah and T Abdeljawad, Adv Differ Equ. 249, 2020 (2020)

    Google Scholar 

  38. W Werner, Math. Computation 43, 205 (1984)

    Article  Google Scholar 

  39. T F Krogh, Math. Computation 24, 185 (1970)

    Article  Google Scholar 

  40. M Toufik and A Atangana, The European Physical J. Plus 132, 444 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

The first author, Rajarama Mohan Jena acknowledges the Department of Science and Technology, Government of India, for providing an INSPIRE Fellowship (IF170207).

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Authors and Affiliations

  1. Department of Mathematics, C. V. Raman Global University, Bhubaneswar, 752 054, India

    Rajarama Mohan Jena & Snehashish Chakraverty

  2. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, Guangxi, People’s Republic of China

    Shengda Zeng

  3. Faculty of Mathematics and Computer Science, Jagiellonian University in Krakow, ul. Lojasiewicza 6, 30348, Krakow, Poland

    Shengda Zeng

  4. Departement of Mathematics, FPT University, Education Zone, Hoa Lac High Tech Park, Thach That Ward, Hanoi, Vietnam

    Van Thien Nguyen

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  1. Rajarama Mohan Jena
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  2. Snehashish Chakraverty
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  3. Shengda Zeng
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  4. Van Thien Nguyen
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Correspondence to Snehashish Chakraverty.

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Jena, R.M., Chakraverty, S., Zeng, S. et al. Non-singular kernel-based time-fractional order Covid-19 mathematical model with vaccination. Pramana - J Phys 97, 177 (2023). https://doi.org/10.1007/s12043-023-02624-y

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  • DOI: https://doi.org/10.1007/s12043-023-02624-y

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