A hybrid fractional COVID-19 model with general population mask use: Numerical treatments

Sweilam, N. H.; AL–Mekhlafi, S.M.; Almutairi, Alanoud; Băleanu, Dumitru

doi:10.1016/j.aej.2021.01.057

Cited by 15 publications

(6 citation statements)

References 20 publications

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“…We present three generalized stochastic fractional techniques to solve the stochastic fractional-order system (15), namely, Euler, Runge-Kutta and a nonstandard finitedifference (NSFD) scheme. The first two are already standard techniques which are well known in the literature [32,33]. The third model is a new technique which is constructed using a non-local approach [34].…”

Section: Numerical Modelmentioning

confidence: 99%

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Ahmed

Macías‐Díaz

Raza³

et al. 2021

Axioms

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Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R0<1. A similar result is obtained for the endemic equilibrium when R0>1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge–Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note.

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Section: Numerical Modelmentioning

confidence: 99%

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Ahmed

Macías‐Díaz

Raza³

et al. 2021

Axioms

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“…Some scientific studies on fractional order optimal control problems have been proposed in previous studies. [21][22][23][24][25] For further learning, the interested researchers can refer to earlier research. [26][27][28][29][30] Motivated from the above facts, the optimal reachability problem for the fractional dynamical systems in terms of 𝜓-Hilfer derivative is not yet studied.…”

Section: Introductionmentioning

confidence: 99%

“…Similarly, Rakhshan and Effati 20 solve FOCP in the Caputo sense using Laplace transforms and the Chebyshev–Gauss collocation method. Some scientific studies on fractional order optimal control problems have been proposed in previous studies 21–25 . For further learning, the interested researchers can refer to earlier research 26–30 …”

Section: Introductionmentioning

confidence: 99%

Fractional optimal reachability problems withψ‐Hilfer fractional derivative

Vellappandi¹,

Govindaraj²,

Sousa

2022

Math Methods in App Sciences

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The aim of this article is to investigate the optimal reachability problem in terms of the 𝜓-Hilfer fractional derivative for a fractional dynamical system.Euler-Lagrange equations are used to obtain the necessary optimality constraints for the fractional optimal reachability problem (FORP). In terms of the 𝜓-Hilfer fractional derivative, we developed the predictor-corrector algorithm to provide numerical solutions to the FORP. Three numerical examples are provided to show the correctness of theoretical outputs.

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“…A mathematical study of the infected cases in Saudi Arabia has been investigated in [25] . A COVID-19 infection model with the use of the face mask has been studied in [26] . A confection model to study cholera and COVID-19 and its dynamical analysis have been given in [27] .…”

Section: Introductionmentioning

confidence: 99%

Application of piecewise fractional differential equation to COVID-19 infection dynamics

Alrihieli

Algehyne

et al. 2022

Results in Physics

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A hybrid fractional COVID-19 model with general population mask use: Numerical treatments

Cited by 15 publications

References 20 publications

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Fractional optimal reachability problems withψ‐Hilfer fractional derivative

Application of piecewise fractional differential equation to COVID-19 infection dynamics

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