Modeling and simulation of the novel coronavirus in Caputo derivative

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

doi:10.1016/j.rinp.2020.103588

Cited by 54 publications

(33 citation statements)

References 21 publications

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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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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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“…A novel coronavirus model has been recently introduced in [ 25 ] using the Caputo derivative. Recently, in [ 26 ], the authors have presented a numerical investigation of fractional COVID-19 model in fractional derivative. More recently, the authors have analyzed the dynamics of corona virus infection through non-integer-order model in [ 27 ].…”

Section: Introductionmentioning

confidence: 99%

A robust study on 2019-nCOV outbreaks through non-singular derivative

2021

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The new coronavirus disease is still a major panic for people all over the world. The world is grappling with the second wave of this new pandemic. Different approaches are taken into consideration to tackle this deadly disease. These approaches were suggested in the form of modeling, analysis of the data, controlling the disease spread and clinical perspectives. In all these suggested approaches, the main aim was to eliminate or decrease the infection of the coronavirus from the community. Here, in this paper, we focus on developing a new mathematical model to understand its dynamics and possible control. We formulate the model first in the integer order and then use the Atangana–Baleanu derivative concept with a non-singular kernel for its generalization. We present some of the necessary mathematical aspects of the fractional model. We use a nonlinear fractional Lyapunov function in order to present the global asymptotical stability of the model at the disease-free equilibrium. In order to solve the model numerically in the fractional case, we use an efficient modified Adams–Bashforth scheme. The resulting iterative scheme is then used to demonstrate the detailed simulation results of the ABC mathematical model to examine the importance of the memory index and model parameters on the transmission and control of COVID-19 infection.

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“…The spread of coronavirus in South Africa and Turkey with detailed statistical and mathematical results is studied in [ 26 ]. Recently, the authors have studied the analysis of coronavirus model in fractional derivative [ 27 ]. The use of quarantine and isolations in the modeling of coronavirus is investigated in [ 28 ].…”

Section: Introductionmentioning

confidence: 99%

A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load

et al. 2021

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COVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the COVID-19 infection is becoming very harmful for the human community and causing financial loses to their economy. No proper vaccine for this infection has been introduced in the market in order to treat the infected people. Various approaches have been implemented recently to study the dynamics of this novel infection. Mathematical models are one of the effective tools in this regard to understand the transmission patterns of COVID-19. In the present paper, we formulate a fractional epidemic model in the Caputo sense with the consideration of quarantine, isolation, and environmental impacts to examine the dynamics of the COVID-19 outbreak. The fractional models are quite useful for understanding better the disease epidemics as well as capture the memory and nonlocality effects. First, we construct the model in ordinary differential equations and further consider the Caputo operator to formulate its fractional derivative. We present some of the necessary mathematical analysis for the fractional model. Furthermore, the model is fitted to the reported cases in Pakistan, one of the epicenters of COVID-19 in Asia. The estimated value of the important threshold parameter of the model, known as the basic reproduction number, is evaluated theoretically and numerically. Based on the real fitted parameters, we obtained $\mathcal{R}_{0} \approx 1.50$ R 0 ≈ 1.50 . Finally, an efficient numerical scheme of Adams–Moulton type is used in order to simulate the fractional model. The impact of some of the key model parameters on the disease dynamics and its elimination are shown graphically for various values of noninteger order of the Caputo derivative. We conclude that the use of fractional epidemic model provides a better understanding and biologically more insights about the disease dynamics.

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Modeling and simulation of the novel coronavirus in Caputo derivative

Cited by 54 publications

References 21 publications

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

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

A robust study on 2019-nCOV outbreaks through non-singular derivative

A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load

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