Mathematical modeling and optimal control of the COVID-19 dynamics

Shen, Zhongliang; Chu, Yu‐Ming; Khan, Muhammad Altaf; Muhammad, Shabbir; Al‐Hartomy, Omar A.; Higazy, M.

doi:10.1016/j.rinp.2021.105028

Cited by 109 publications

(56 citation statements)

References 17 publications

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“…A fractional model in ABC operator in astrophysics is discussed in [26]. A recent study is conducted for the understanding of coronavirus infection and its controls [27]. A mathematical model in non-singular order to investigate the coronavirus infection is considered in [28].…”

Section: Introductionmentioning

confidence: 99%

A mathematical model for SARS-CoV-2 in variable-order fractional derivative

DarAssi

Safi

Khan

et al. 2022

Eur. Phys. J. Spec. Top.

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A new coronavirus mathematical with hospitalization is considered with the consideration of the real cases from March 06, 2021 till the end of April 30, 2021. The essential mathematical results for the model are presented. We show the model stability when in the absence of infection. We show that the system is stable locally asymptotically when at infection free state. We also show that the system is globally asymptotically stable in the disease absence when . Data have been used to fit accurately to the model and found the estimated basic reproduction number to be . Some graphical results for the effective parameters are drawn for the disease elimination. In addition, a variable-order model is introduced, and so as to handle the outbreak effectively and efficiently, a genetic algorithm is used to produce high-quality control. Numerical simulations clearly show that decision-makers may develop helpful and practical strategies to manage future waves by implementing optimum policies.

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Section: Introductionmentioning

confidence: 99%

A mathematical model for SARS-CoV-2 in variable-order fractional derivative

DarAssi

Safi

Khan

et al. 2022

Eur. Phys. J. Spec. Top.

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“…We have also the so-called Atangana-Baleanu fractional operator and the Caputo-Fabrizio derivative which are known as the fractional operators with non-singular kernels [4,5]. These singular and non-singular derivatives appear in many papers with applications to physical modeling [2,6,7], biological modeling [8,9,10,11,12,13,14], sciences and engineering modeling [15,16,17,18,19], mathematical physics modeling [20,21,22,23,24,25,26], physics modeling [24,27] and others domains [28,29,30,31,32]. The field of fractional calculus is interesting but there also exist many questions without responses.…”

Section: Introductionmentioning

confidence: 99%

Second-grade fluid with Newtonian heating under Caputo fractional derivative: analytical investigations via Laplace transforms

Sene

2022

mmnsa

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In this paper, we consider the constructive equations of the fractional second-grade fluid. The considered fluid model is described by the Caputo derivative. The problem consists to determine the exact analytical solution using the Laplace transform method. The influence of the order of the used fractional operator has been presented in this paper. We also analyze the influence of the Prandtl number in the dynamics of the temperature distribution according to the variation of the order of the Caputo derivative. The impact of the second-grade parameter and the Grashof number in the dynamics of the velocity has been presented and discussed. The influences of the parameters used in the modeling have been interpreted in terms of a fractional context. In general, it is shown that the order of the fractional operator influences the diffusivity of the considered fluid. This influence can cause an increase or decrease in the temperature and velocity distributions. The main findings of the paper have been illustrated using the graphical representations of the considered distributions according to the order of the fractional operator.

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“…Before we formulate a new mathematical model to study the impact of SARS-COV-2 with reinfection, we first highlight some mathematical models that addressed the COVID-19 infection. Mathematical modeling and its optimal control analysis to curb the coronavirus infection is considered in Shen et al (2021) . A case study related to COVID-19 in Thailand using a mathematical model is given in Riyapan et al (2021) .…”

Section: Introductionmentioning

confidence: 99%