Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator

Redhwan, Saleh S.; Abdo, Mohammed S.; Shah, Kamal; Abdeljawad, Thabet; Dawood, Shaheenah; Abdo, Hakim A.; Shaikh, Sadikali L.

doi:10.1016/j.rinp.2020.103610

Cited by 31 publications

(15 citation statements)

References 49 publications

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“…The existence and uniqueness of solutions for different classes of fractional differential equations (FDEs) with initial or boundary conditions have been studied by several researchers; see [30][31][32][33][34][35][36][37][38] and the references therein. Some recent contributions on FDEs involving ABC-FDs can be found in the following articles series: [39][40][41][42][43][44][45][46][47][48][49]. For instance, AB-Caputo fractional IVP is one of the studied problems by Jarad et al [39], and has the form ⎧ ⎨ ⎩ ABC D ϑ a + ς(r) = f (r, ς(r)), r ∈ [a, T], 0 < ϑ ≤ 1, ς(a) = ς a .…”

Section: Introductionmentioning

confidence: 99%

On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions

et al. 2021

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In this paper, we consider two classes of boundary value problems for nonlinear implicit differential equations with nonlinear integral conditions involving Atangana–Baleanu–Caputo fractional derivatives of orders $0<\vartheta \leq 1$ 0 < ϑ ≤ 1 and $1<\vartheta \leq 2$ 1 < ϑ ≤ 2 . We structure the equivalent fractional integral equations of the proposed problems. Further, the existence and uniqueness theorems are proved with the aid of fixed point theorems of Krasnoselskii and Banach. Lastly, the paper includes pertinent examples to justify the validity of the results.

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Section: Introductionmentioning

confidence: 99%

On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions

et al. 2021

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“… [23] proposed a model based on fixed point and establish related existence results under ABC derivative with fractional order. [24] studied a mathematical model based on a fractional Atangana-Baleanu (AB) operator. [25] presented a model with three compartments (susceptible, infected and recovered) which is extended into a stochastic model in [26] .…”

Section: Introductionmentioning

confidence: 99%

Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo

et al. 2021

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This paper deals with modeling and simulation of the novel coronavirus in which the infectious individuals are divided into three subgroups representing three forms of infection. The rigorous analysis of the mathematical model is provided. We provide also a rigorous derivation of the basic reproduction number . For , we prove that the Disease Free Equilibium (DFE) is Globally Asymptotically Stable (GAS), thus COVID-19 extincts; whereas for , we found the co-existing phenomena under some assumptions and parametric values. Elasticity indices for with respect to different parameters are calculated with baseline parameter values estimated. We also prove that a transcritical bifurcation occurs at . Taking into account the control strategies like screening, treatment and isolation (social distancing measures), we present the optimal control problem of minimizing the cost due to the application of these measures. By reducing the values of some parameters, such as death rates (representing a management effort for all categories of people) and recovered rates (representing the action of reduction in transmission, improved screening, treatment for individuals diagnosed positive to COVID-19 and the implementation of barrier measures limiting contamination for undiagnosed individuals), it appears that after days, the peak of the pandemic is reached and shows that by continuing with this strategy, COVID-19 could be eliminated in the population.

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“…The proposed outbreak of this virus effectively catches the time line for the COVID‐19 disease conceptual model 26–28 . Analysis of a mathematical model for the spread of the COVID‐19 disease by different mathematical techniques is discussed 29–34 . For more details see other works 35–38 …”

Section: Introductionmentioning

confidence: 99%

Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

Farman

Aslam

Akgül

et al. 2021

Math Methods in App Sciences

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Different countries of the world are facing a serious pandemic of corona virus disease (COVID‐19). One of the most typical treatments for COVID‐19 is social distancing, which includes lockdown; it will help to decrease the number of contacts for undiagnosed individuals. The main aim of this article is to construct and evaluate a fractional‐order COVID‐19 epidemic model with quarantine and social distancing. Laplace homotopy analysis method is used for a system of fractional differential equation (FDEs) with Caputo and Atangana–Baleanu–Caputo (ABC) fractional derivative. By applying the ABC and Caputo derivative, the numerical solution for fractional‐order COVID‐19 epidemic model is achieved. The uniqueness and existence of the solution is checked by Picard–Lindelof's method. The proposed fractional model is demonstrated by numerical simulation which is useful for the government to control the spread of disease in a practical way.

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Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator

Cited by 31 publications

References 49 publications

On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions

On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions

Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo

Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

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