Numerical investigations on<scp>COVID</scp>‐19 model through singular and non‐singular fractional operators

Kumar, Sunil; Chauhan, R.P.; Momani, Shaher; Hadid, Samir

doi:10.1002/num.22707

Cited by 117 publications

(30 citation statements)

References 51 publications

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“…Moreover, the Ulam types stability was presented by using nonlinear analysis. Some other recent relevant literature can be found in [26] , [27] , [28] .…”

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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“…Moreover, the Ulam types stability was presented by using nonlinear analysis. Some other recent relevant literature can be found in [26] , [27] , [28] .…”

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

View full text Add to dashboard Cite

show abstract

“…The authors in [20] , provided a detailed theoretical and numerical analysis of the proposed model. A comparative numerical study of a COVID-19 mathematical model based on singular and non-singular kernel has been conducted in [21] . Recently, the dynamics of COVID-19 pandemic have been addressed with the help of ABC fractional operator in [22] .…”

Section: Introductionmentioning

confidence: 99%

Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach

et al. 2022

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Super-spreaders of the novel coronavirus disease (or COVID-19) are those with greater potential for disease transmission to infect other people. Understanding and isolating the super-spreaders are important for controlling the COVID-19 incidence as well as future infectious disease outbreaks. Many scientific evidences can be found in the literate on reporting and impact of super-spreaders and super-spreading events on the COVID-19 dynamics. This paper deals with the formulation and simulation of a new epidemic model addressing the dynamics of COVID-19 with the presence of super-spreader individuals. In the first step, we formulate the model using classical integer order nonlinear differential system composed of six equations. The individuals responsible for the disease transmission are further categorized into three sub-classes, i.e., the symptomatic, super-spreader and asymptomatic. The model is parameterized using the actual infected cases reported in the kingdom of Saudi Arabia in order to enhance the biological suitability of the study. Moreover, to analyze the impact of memory index, we extend the model to fractional case using the well-known Caputo–Fabrizio derivative. By making use of the Picard-Lindelöf theorem and fixed point approach, we establish the existence and uniqueness criteria for the fractional-order model. Furthermore, we applied the novel fractal-fractional operator in Caputo–Fabrizio sense to obtain a more generalized model. Finally, to simulate the models in both fractional and fractal-fractional cases, efficient iterative schemes are utilized in order to present the impact of the fractional and fractal orders coupled with the key parameters (including transmission rate due to super-spreaders) on the pandemic peaks.

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“…The well-known differential operators with fractional order include the classical Caputo with power law index [9] , Caputo-Fabrizio with exponential kernel [10] and Atangana-Baleanu-Caputo (ABC) with Mittag-Leffler kernel [11] . The application of fractional operator can be found in formulating real-world problems of science and engineering especially in epidemiology [12] , [13] , [14] , [15] , [16] , [17] . Numerous mathematical models based on non-integer order differential systems have been proposed recently to analyze the dynamical behavior of the novel coronavirus disease.…”

Section: Introductionmentioning

confidence: 99%

“…The dynamics of novel mathematical model based on the Caputo operator coupled with real data from Wuhan China was studied in [23] . An extensive analysis both theoretically and numerically of a fractional COVID-19 mathematical model was carried out in [14] . The authors in [14] used three different fractional order operators to analyze the dynamics of novel COVID-19.…”

Section: Introductionmentioning

confidence: 99%

“…An extensive analysis both theoretically and numerically of a fractional COVID-19 mathematical model was carried out in [14] . The authors in [14] used three different fractional order operators to analyze the dynamics of novel COVID-19. Recently, a modified fractional modeling approach has been adopted to investigate the impact of various control measures and viral transmission on the dynamics of COVID-19 outbreak in Saudi Arabia [24] .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study

Liu

Ullah

Alshehri

et al. 2021

Chaos, Solitons & Fractals

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Numerical investigations onCOVID‐19 model through singular and non‐singular fractional operators

Cited by 117 publications

References 51 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

Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach

Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study

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