Numerical and theoretical analysis of an awareness COVID-19 epidemic model via generalized Atangana-Baleanu fractional derivative

Baba, Isa Abdullahi; Ahmed, Idris Adewale; Al‐Mdallal, Qasem M.; Jarad, Fahd; Yunusa, Salisu

doi:10.17512/jamcm.2022.1.01

Cited by 6 publications

(2 citation statements)

References 8 publications

(11 reference statements)

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“…This virus was first reported at the end of 2019 in Wuhan, China. Then, it was reported in other places in China surprisingly [2]. In three months, the disease was transmitted in many countries of the world.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

Sadek¹,

Sadek²,

Alaoui³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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In this work, we present a model that uses the fractional order Caputo derivative for the novel Coronavirus disease 2019 with different hospitalization strategies for severe and mild cases and incorporate an awareness program. We generalize the SEIR model of the spread of COVID-19 with a private focus on the transmissibility of people who are aware of the disease and follow preventative health measures and people who are ignorant of the disease and do not follow preventive health measures. Moreover, individuals with severe, mild symptoms and asymptomatically infected are also considered. The basic reproduction number (R 0 ) and local stability of the disease-free equilibrium (DFE) in terms of R 0 are investigated. Also, the uniqueness and existence of the solution are studied. Numerical simulations are performed by using some real values of parameters. Furthermore, the immunization of a sample of aware susceptible individuals in the proposed model to forecast the effect of the vaccination is also considered. Also, an investigation of the effect of public awareness on transmission dynamics is one of our aim in this work. Finally, a prediction about the evolution of COVID-19 in 1000 days is given. For the qualitative theory of the existence of a solution, we use some tools of nonlinear analysis, including Lipschitz criteria. Also, for the numerical interpretation, we use the Adams-Moulton-Bashforth procedure. All the numerical results are presented graphically.

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Section: Introductionmentioning

confidence: 99%

Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

Sadek¹,

Sadek²,

Alaoui³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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“…Recent literature on the application of fractional derivative for studying the Covid‐19 virus includes Yao et al, 10 with a study on fractional‐order Covid‐19 model with transmission route infected through the environment, while Baba et al 11 employed the generalized Atangana‐Baleanu fractional derivative to investigate the awareness Covid‐19 epidemic model. A Fractional‐order Compartmental model of Covid‐19 vaccination with the fear factor was presented by Chatterjee et al 12 Ali et al 13 presented a fractional‐order mathematical model for Covid‐19 outbreak with the effect of symptomatic and asymptomatic transmissions, and Baba et al 14 assessed the efficiency of face‐mask to the community transmission of Covid‐19 using Fractional dynamical model.…”

Section: Introductionmentioning

confidence: 99%

Some novel mathematical analysis on the fractional‐order 2019‐nCoV dynamical model

Owoyemi¹,

Sulaiman

Kumar

et al. 2022

Math Methods in App Sciences

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Since December 2019, the whole world has been facing the big challenge of Covid‐19 or 2019‐nCoV. Some nations have controlled or are controlling the spread of this virus strongly, but some countries are in big trouble because of their poor control strategies. Nowadays, mathematical models are very effective tools to simulate outbreaks of this virus. In this research, we analyze a fractional‐order model of Covid‐19 in terms of the Caputo fractional derivative. First, we generalize an integer‐order model to a fractional sense, and then, we check the stability of equilibrium points. To check the dynamics of Covid‐19, we plot several graphs on the time scale of daily and monthly cases. The main goal of this content is to show the effectiveness of fractional‐order models as compared to integer‐order dynamics.

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A high‐order predictor–corrector method for initial value problems with fractional derivative involving Mittag–Leffler kernel

Aljhani

Noorani

Douaifia

et al. 2023

Math Methods in App Sciences

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In this paper, we propose a numerical scheme of the predictor–corrector type for solving nonlinear fractional initial value problems; the chosen fractional derivative is called the Atangana–Baleanu derivative defined in Caputo sense (ABC). This proposed method is based on Lagrangian quadratic polynomials to approximate the nonlinearity implied in the Volterra integral, which is obtained by reducing the given fractional differential equation via the properties of the ABC‐fractional derivative. Through this technique, we get corrector formula with high accuracy, which is implicit, as well as predictor formula, which is explicit and has the same precision order as the corrective formula. On the other hand, the so‐called memory term is computed only once for both prediction and correction phases, which indicates the low cost of the proposed method. Also, the error bound of the proposed numerical scheme is offered. Furthermore, numerical experiments are presented in order to assess the accuracy of the new method on two differential equations. Moreover, a case study is considered where the proposed predictor–corrector scheme is used to obtain approximate solutions of a coupled nonautonomous ABC‐fractional differential system.

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Numerical and theoretical analysis of an awareness COVID-19 epidemic model via generalized Atangana-Baleanu fractional derivative

Cited by 6 publications

References 8 publications

Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

Some novel mathematical analysis on the fractional‐order 2019‐nCoV dynamical model

A high‐order predictor–corrector method for initial value problems with fractional derivative involving Mittag–Leffler kernel

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