Abstract
We consider a SEAIR epidemic model with Atangana–Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Optimal control analysis and simulation show that the control strategy designed is operative in reducing the number of cases in different compartments. Moreover, simulating the optimal profile revealed that reducing the fractional-order from 1 leads to the need for quick starting of the application of the designed control strategy at the maximum possible level and maintaining it for the majority of the period of the pandemic.
Highlights
Epidemiological mathematical models provide several aspects for understanding the dynamics of the spread of an epidemic and suggestions of effective control strategies
Other early mathematical models in epidemiology were introduced in 1927 when Kermack and McKendrick published a series of papers that described the dynamics of disease transmission in terms of a system of differential equations [2]
2 Model description and formulation we develop the Atangana–Baleanu fractional derivative representation of the SEAIR endemic mathematical model
Summary
Epidemiological mathematical models provide several aspects for understanding the dynamics of the spread of an epidemic and suggestions of effective control strategies. Fractional calculus is a branch of mathematical analysis that studies calculus of derivatives and integrals of arbitrary orders. Kahan et al [18] investigated a COVID-19 mathematical model with a fractal-fractional model in the sense of Atangana–Baleanu fractional operator. An insight on the existence and uniqueness of the solution to a COVID-19 mathematical model using fractional and fractional-fractal operators and fixed point theorem is performed in [21]. The Atangana–Baleanu fractional derivative operator involving the Mittag-Leffler kernel is used to analyze SEIRA mathematical model in [32]. The authors argue that optimal control analysis of mathematical models in the sense of Atangana–Baleanu fractional operators is uncommon in the existing literature. We perform a numerical simulation verifying the effect of the designed control strategy for different values of fractional order and different compartments of the model. The AtanganaBaleanu (AB) fractional derivative in Caputo type of order η is given by [25, 26, 33]
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