Modeling and analysis of the dynamics of novel coronavirus (COVID-19) with Caputo fractional derivative

Ali, Aatif; Alshammari, Fehaid Salem; Islam, Saeed; Khan, Muhammad Altaf; Ullah, Saif

doi:10.1016/j.rinp.2020.103669

Cited by 65 publications

(23 citation statements)

References 31 publications

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“…Finally, they compared it with the Adams–Bashforth predictor–corrector scheme in [19] . Ali et al [20] discussed the dynamic of the COVID-19 model of fractional order and investigate the stability analysis using the Lyapunov function. A fractional-order model for COVID-19 model is suggest by Oud et al [21] , considering the impact of quarantine, isolation and environment.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission

Khan¹,

Amin²,

Ullah³

et al. 2022

Alexandria Engineering Journal

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The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The infection is very destructive to human lives and caused millions of deaths. Various approaches have been made recently to understand the complex dynamics of COVID-19. The mathematical modeling approach is one of the considerable tools to study the disease spreading pattern. In this article, we develop a fractional order epidemic model for COVID-19 in the sense of Caputo operator. The model is based on the effective contacts among the population and environmental impact to analyze the disease dynamics. The fractional models are comparatively better in understanding the disease outbreak and providing deeper insights into the infectious disease dynamics. We first consider the classical integer model studied in recent literature and then we generalize it by introducing the Caputo fractional derivative. Furthermore, we explore some fundamental mathematical analysis of the fractional model, including the basic reproductive number and equilibria stability utilizing the Routh-Hurwitz and the Lyapunov function approaches. Besides theoretical analysis, we also focused on the numerical solution. To simulate the model, we use the well-known generalized Adams–Bashforth Moulton Scheme. Finally, the influence of some of the model essential parameters on the dynamics of the disease is demonstrated graphically.

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission

Khan¹,

Amin²,

Ullah³

et al. 2022

Alexandria Engineering Journal

Self Cite

View full text Add to dashboard Cite

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“…Moreover, some researchers used fractional order in epidemic models to model the spread of COVID-19. Fractional order derivative with Mittag-Leffler function as a nonsingular kernel type [17] and Caputo derivative [18][19][20] are used in modeling the transmission of COVID-19. Then [21,22] considered the fractal-fractional derivative in the Atangana-Baleanu sense to obtain the stability of the model, and [23] presented the existence and uniqueness solution of the model via fractal-fractional operators.…”

Section: Introductionmentioning

confidence: 99%

An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia

et al. 2021

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The aim of this research is to construct an SIR model for COVID-19 with fuzzy parameters. The SIR model is constructed by considering the factors of vaccination, treatment, obedience in implementing health protocols, and the corona virus-load. Parameters of the infection rate, recovery rate, and death rate due to COVID-19 are constructed as a fuzzy number, and their membership functions are used in the model as fuzzy parameters. The model analysis uses the generation matrix method to obtain the basic reproduction number and the stability of the model’s equilibrium points. Simulation results show that differences in corona virus-loads will also cause differences in the transmission of COVID-19. Likewise, the factors of vaccination and obedience in implementing health protocols have the same effect in slowing or stopping the transmission of COVID-19 in Indonesia.

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“…We have a lot of examples for the applications of such kind of equations in our life as in fluid mechanics, [1][2][3] image processing, 4 biology, [5][6][7][8][9][10][11][12] engineering, [13][14][15] physics, [16][17][18][19][20] electrical circuits and filters, [21][22][23][24][25][26][27][28][29][30][31][32] and others. [33][34][35][36] Definition 1. The Liouville-Caputo fractional derivative of order ν, D ν of a function φ can be defined by D ν φðtÞ ¼ 1 Γðℓ À νÞ ð t 0 φ ðℓÞ ðτÞ ðt À τÞ νÀℓþ1 dτ, ν > 0, ℓ À 1 < ν ≤ ℓ, ℓ ℕ, t > 0, where Γ(.)…”

Section: Introductionmentioning

confidence: 99%

Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method

Khader

Gómez-Aguilar²,

Adel

2021

Circuit Theory & Apps

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In the presented work, we present an accurate procedure, which is the spectral method, to find a solution to a certain class of the very important fractional (described by the Liouville-Caputo sense) models of the electrical RL, RC, and RLC circuits. This method is collocated using some important advantages of the generalized Legendre polynomials to obtain the numerical solution for these models. Besides, we compare the approximate solutions that are obtained using the presented technique for the proposed models with their exact solution in the given numerical examples.

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Modeling and analysis of the dynamics of novel coronavirus (COVID-19) with Caputo fractional derivative

Cited by 65 publications

References 31 publications

Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission

Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission

An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia

Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method

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