Control of COVID-19 dynamics through a fractional-order model

Bushnaq, Samia; Saeed, Tareq; Torres, Delfim F. M.; Zeb, Anwar

doi:10.1016/j.aej.2021.02.022

Cited by 49 publications

(24 citation statements)

References 39 publications

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“…In Section 3.4, we use the necessary optimality conditions ( 9)-( 11) to numerically solve the optimal control problem ( 4)- (7), both in classical and fractional cases.…”

Section: Fractional Optimal Control Of the Modelmentioning

confidence: 99%

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Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

Rosa

Torres

2022

Axioms

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A fractional-order compartmental model was recently used to describe real data of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons Fractals 144 (2021), Art. 110652]. Here, we modify that model in order to correct time dimensions and use it to investigate the third wave of COVID-19 that occurred in Portugal from December 2020 to February 2021, and that has surpassed all previous waves, both in number and consequences. A new fractional optimal control problem is then formulated and solved, with vaccination and preventive measures as controls. A cost-effectiveness analysis is carried out, and the obtained results are discussed.

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“…In Section 3.4, we use the necessary optimality conditions ( 9)-( 11) to numerically solve the optimal control problem ( 4)- (7), both in classical and fractional cases.…”

Section: Fractional Optimal Control Of the Modelmentioning

confidence: 99%

“…Those dynamics have been modelled and studied by using the concept of fractional-order derivatives. These problems appear in a range of diversified fields of applied sciences, including biology, physics, ecology, and engineering [7,8].…”

Section: Introductionmentioning

confidence: 99%

Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

Rosa

Torres

2022

Axioms

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“…Thus, providing mathematical models to control and predict the behavior of this pandemic is urgent [2]. Recently, many mathematical models related to COVID-19 have been studied [3,4]. In [5], an analysis model of diagnosis and treatment for the COVID-19 pandemic based on medical information fusion was discussed, in [6] a model of the COVID-19 epidemic and predicting its future situation in Ethiopia was studied and in [7] a fractional order COVID-19 model with real-life data application was analyzed.…”

Section: Introductionmentioning

confidence: 99%

A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

2021

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In this paper, a nonlinear fractional order model of COVID-19 is approximated. For this aim, at first we apply the Caputo–Fabrizio fractional derivative to model the usual form of the phenomenon. In order to show the existence of a solution, the Banach fixed point theorem and the Picard–Lindelof approach are used. Additionally, the stability analysis is discussed using the fixed point theorem. The model is approximated based on Indian data and using the homotopy analysis transform method (HATM), which is among the most famous, flexible and applicable semi-analytical methods. After that, the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library, which are based on discrete stochastic arithmetic (DSA), are applied to validate the numerical results of the HATM. Additionally, the stopping condition in the numerical algorithm is based on two successive approximations and the main theorem of the CESTAC method can aid us analytically to apply the new terminations criterion instead of the usual absolute error that we use in the floating-point arithmetic (FPA). Finding the optimal approximations and the optimal iteration of the HATM to solve the nonlinear fractional order model of COVID-19 are the main novelties of this study.

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“…Since some models do not capture well the dynamics, it is considered a fractional principle. Fractal and fractional models have considered, for example in Ndaïrou et al (2021 1 ) and Bushnaq et al (2021 2 ). I would recommend to continue this approach with updated data.…”

mentioning

confidence: 99%

“…Fractal and fractional models have considered, for example in Ndaïrou et al (2021 1 ) and Bushnaq et al (2021 2 ).…”

mentioning

confidence: 99%

Interpreting airborne pandemics spreading using fractal kinetics’ principles

Macheras

Tsekouras

2021

F1000Res

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Introduction The reaction between susceptible and infected subjects has been studied under the well-mixed hypothesis for almost a century. Here, we present a consistent analysis for a not well-mixed system using fractal kinetics’ principles. Methods We analyzed COVID-19 data to get insights on the disease spreading in absence/presence of preventive measures. We derived a three-parameter model and show that the “fractal” exponent h of time larger than unity can capture the impact of preventive measures affecting population mobility. Results The h=1 case, which is a power of time model, accurately describes the situation without such measures in line with a herd immunity policy. The pandemic spread in four model countries (France, Greece, Italy and Spain) for the first 10 months has gone through four stages: stages 1 and 3 with limited to no measures, stages 2 and 4 with varying lockdown conditions. For each stage and country two or three model parameters have been determined using appropriate fitting procedures. The fractal kinetics model was found to be more akin to real life. Conclusion Model predictions and their implications lead to the conclusion that the fractal kinetics model can be used as a prototype for the analysis of all contagious airborne pandemics.

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Control of COVID-19 dynamics through a fractional-order model

Cited by 49 publications

References 39 publications

Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

Interpreting airborne pandemics spreading using fractal kinetics’ principles

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