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Fractional Order Model for the Role of Mild Cases in the Transmission of COVID-19

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  • Baba, Isa Abdullahi
  • Nasidi, Bashir Ahmad

Abstract

Most of the nations with deplorable health conditions lack rapid COVID-19diagnostic test due to limited testing kits and laboratories. The un-diagnosticmild cases (who show no critical sign and symptoms) play the role as a route that spread the infection unknowingly to healthy individuals. In this paper, we present a fractional order SIR model incorporating individual with mild cases as a compartment to become SMIR model. The existence of the solutions of the model is investigated by solving the fractional Gronwall's inequality using the Laplace transform approach. The equilibrium solutions (DFE & Endemic) are found to be locally asymptotically stable, and subsequently the basic reproduction number is obtained. Also the global stability analysis is carried out by constructing Lyapunov function. Lastly, numerical simulations that support analytic solution follow. It was also shown that when the rate of infection of the mild cases increases, there is equivalent increase in the overall population of infected individuals. Hence to curtail the spread of the disease there is need to take care of the Mild cases as well.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920307682
    DOI: 10.1016/j.chaos.2020.110374
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    References listed on IDEAS

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    1. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    2. 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).
    3. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    Cited by:

    1. 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).
    2. Khan, Hasib & Ahmad, Farooq & Tunç, Osman & Idrees, Muhammad, 2022. "On fractal-fractional Covid-19 mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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