A robust study of a piecewise fractional order COVID-19 mathematical model

Zeb, Anwar; Atangana, Abdon; Khan, Zareen A.; Djillali, Salih

doi:10.1016/j.aej.2021.11.039

Cited by 50 publications

(21 citation statements)

References 50 publications

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“…( 2020a , 2020b ); Zeb et al. ( 2022 ). Considering the delay effect in the mathematical modeling of the dynamics of the virus implies right conclusions.…”

Section: Introductionmentioning

confidence: 99%

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Modeling the stochastic within-host dynamics SARS-CoV-2 infection with discrete delay

2022

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In this paper, a new mathematical model that describes the dynamics of the within-host COVID-19 epidemic is formulated. We show the stochastic dynamics of Target-Latent-Infected-Virus free within the human body with discrete delay and noise. Positivity and uniqueness of the solutions are established. Our study shows the extinction and persistence of the disease inside the human body through the stability analysis of the disease-free equilibrium $$E_0$$ E 0 and the endemic equilibrium $$E^*$$ E ∗ , respectively. Moreover, we show the impact of delay tactics and noise on the extinction of the disease. The most interesting result is even if the deterministic system is inevitably pandemic at a specific point, extinction will become possible in the stochastic version of our model.

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“…( 2020a , 2020b ); Zeb et al. ( 2022 ). Considering the delay effect in the mathematical modeling of the dynamics of the virus implies right conclusions.…”

Section: Introductionmentioning

confidence: 99%

“…Many works have dealt with various viruses by mathematical models inside the human body, see Li and Xiao (2011); Zeb et al (2020); Best and Perelson (2018); Zhang et al (2020aZhang et al ( , 2020b; Zeb et al (2022). Considering the delay effect in the mathematical modeling of the dynamics of the virus implies right conclusions.…”

Section: Introductionmentioning

confidence: 99%

Modeling the stochastic within-host dynamics SARS-CoV-2 infection with discrete delay

2022

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“…The concept of the piecewise derivative and integral operator is used with different fractional derivatives to investigate an SIR mathematical model of COVID-19 in [17]. Zeb et al [18] investigated a five-dimensional compartmental model of COVID-19 with the concept of piecewise derivative and integral operators combining the Caputo-Fabrizio, classical, and stochastic differential equations. A mathematical model representing an interaction in a food web is considered, and the concept of piecewise differential and integral operator is imposed for investigation in [19].…”

Section: Introductionmentioning

confidence: 99%

On a Mathematical Model of Tumor‐Immune Interaction with a Piecewise Differential and Integral Operator

Rezapour

Deressa

Mukharlyamov

et al. 2022

Journal of Mathematics

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The representation of mathematical models via piecewise differential and integral operators for dynamic systems has this potential to capture cross-over behaviors such as a passage from deterministic to randomness which can be exhibited by different systems. A 3D mathematical model, similar to the prey-predator system, of tumor-immune interaction with piecewise differential and integral operators is developed and analyzed. Three different scenarios, namely, cross-overs from deterministic to randomness, the Mittag-Leffler law to randomness, and a cross-over behavior from fading memory to the power-law and a random process, are considered. The existence, uniqueness, positivity, and boundedness of the solutions of the systems are proved via the linear growth and Lipschitz conditions. The numerical approximations by Toufik, Atangana, and Araz are used for approximation of solutions and simulation of the piecewise models in different scenarios. From the nondimensionalized version of the 3D model representation, it is shown that the parameter values have an impact on the growth of tumor cells, and activating the proliferation of the resting cells has negatively affected the development of tumor cells. Moreover, the dynamics of tumor-immune interaction exhibited a cross-over behavior, and this behavior is exposed by the piecewise modeling approach used for the representations.

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“…Different approaches for predicting the spread of COVID-19 epidemic in different countries outlined in recent publication [15][16][17][18][19] are summarized in the next paragraph.…”

Section: Introductionmentioning

confidence: 99%

“…The main propagation of the COVID-19 to find the control for the rapid spread of this Page 2 of 12 Hamed Beni-Suef Univ J Basic Appl Sci (2022) 11:98 viral disease in real life a discrete form of the model considers the dynamics of population in four classes [17]. A robust study of a piecewise fractional-order COVID-19 mathematical model with quarantine class and vaccination using SEIQR epidemic model [18] is performed. The evolution of the COVID-19 infection cases is predicted the spread of COVID-19 disease in Algeria and India using the least square method [19].…”

Section: Introductionmentioning

confidence: 99%

Modeling of corona virus and its application in confocal microscopy

Hamed

2022

Beni-Suef Univ J Basic Appl Sci

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Background The proposal of spiky apertures showed resolution improvement compared with the circular apertures. Three models of corona virus are given. The 1st model consists of uniform circular aperture provided with 8 spikes while the 2nd model has 16 spikes for the same uniform circular aperture. The 3rd model has circular linear distribution with 8 spikes. Results The Normalized Point Spread Function (PSF) or the impulse response is computed for the three models using fast Fourier transform technique. In addition, the autocorrelation function corresponding to these apertures is calculated and compared with that corresponding to the ordinary circular and conic apertures. Coronavirus image is used as an object in the formation of images using confocal scanning laser microscope provided with suggested models. The fabricated MATLAB code is used to compute and plot all images and line plots. Conclusions The PSF plots are computed from Eqs. (8) and (12) using MATLAB code showing narrower cutoff in the PSF for spiky aperture compared with that corresponding to the uniform circular aperture and modulated linear and quadratic apertures. Hence, I reached resolution improvement in the case of spiky aperture.

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A robust study of a piecewise fractional order COVID-19 mathematical model

Cited by 50 publications

References 50 publications

Modeling the stochastic within-host dynamics SARS-CoV-2 infection with discrete delay

Modeling the stochastic within-host dynamics SARS-CoV-2 infection with discrete delay

On a Mathematical Model of Tumor‐Immune Interaction with a Piecewise Differential and Integral Operator

Modeling of corona virus and its application in confocal microscopy

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