A fractional mathematical model for COVID-19 outbreak transmission dynamics with the impact of isolation and social distancing

Ihtisham Ul Haq; Nigar Ali; Shabir Ahmad; Ihtisham Ul Haq; Nigar Ali; Shabir Ahmad

doi:10.3934/mmc.2022022

Mathematical Modelling and Control

2022, Volume 2, Issue 4: 228-242. doi: 10.3934/mmc.2022022

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A fractional mathematical model for COVID-19 outbreak transmission dynamics with the impact of isolation and social distancing

Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan

Received: 26 July 2022 Revised: 06 December 2022 Accepted: 18 December 2022 Published: 26 December 2022

The Covid illness (COVID-19), which has emerged, is a highly infectious viral disease. This disease led to thousands of infected cases worldwide. Several mathematical compartmental models have been examined recently in order to better understand the Covid disease. The majority of these models rely on integer-order derivatives, which are incapable of capturing the fading memory and crossover behaviour observed in many biological phenomena. Similarly, the Covid disease is investigated in this paper by exploring the elements of COVID-19 pathogens using the non-integer Atangana-Baleanu-Caputo derivative. Using fixed point theory, we demonstrate the existence and uniqueness of the model's solution. All basic properties for the given model are investigated in addition to Ulam-Hyers stability analysis. The numerical scheme is based on Lagrange's interpolation polynomial developed to estimate the model's approximate solution. Using real-world data, we simulate the outcomes for different fractional orders in Matlab to illustrate the transmission patterns of the present Coronavirus-19 epidemic through graphs.
- fractional derivatives,
- fractional integral,
- Hyers Ulams stability,
- Lagrange's interpolation
Citation: Ihtisham Ul Haq, Nigar Ali, Shabir Ahmad. A fractional mathematical model for COVID-19 outbreak transmission dynamics with the impact of isolation and social distancing[J]. Mathematical Modelling and Control, 2022, 2(4): 228-242. doi: 10.3934/mmc.2022022

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Abstract

The Covid illness (COVID-19), which has emerged, is a highly infectious viral disease. This disease led to thousands of infected cases worldwide. Several mathematical compartmental models have been examined recently in order to better understand the Covid disease. The majority of these models rely on integer-order derivatives, which are incapable of capturing the fading memory and crossover behaviour observed in many biological phenomena. Similarly, the Covid disease is investigated in this paper by exploring the elements of COVID-19 pathogens using the non-integer Atangana-Baleanu-Caputo derivative. Using fixed point theory, we demonstrate the existence and uniqueness of the model's solution. All basic properties for the given model are investigated in addition to Ulam-Hyers stability analysis. The numerical scheme is based on Lagrange's interpolation polynomial developed to estimate the model's approximate solution. Using real-world data, we simulate the outcomes for different fractional orders in Matlab to illustrate the transmission patterns of the present Coronavirus-19 epidemic through graphs.

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