Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay

Ikram, Rukhsar; Khan, Amir; Zahri, Mostafa; Saeed, Anwar; Yavuz, Mehmet; Kumam, Poom

doi:10.1016/j.compbiomed.2021.105115

Cited by 62 publications

(23 citation statements)

References 24 publications

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“…We recover the same velocity field expressions for all cases which are discussed above by taking Gm = 0 in Equations ( 43), ( 46)-(48) as X. H. Zhang et al [44] investigated in Equations ( 26), ( 33), ( 35) and (37). All these results validate our current results.…”

Section: Ordinary Viscous Fluidsupporting

confidence: 83%

“…substituting the value of T(φ, ξ) from Equation ( 27) and the value of C(φ, ξ) from Equation (37) in Equation ( 40), then after manipulation the solution written in the form ū(φ, ξ) = e 5 e φ √ ξ(1+λξ) + e 6 e −φ √ ξ(1+λξ) − (1 + λξ)Gr f (ξ)…”

Section: Exact Solution Of Fluid Velocitymentioning

confidence: 99%

“…Ozkose et al [34,35] developed a fractional model of tumor-immune system interaction related to lung cancer and also studied the interactions between COVID-19 and diabetes with hereditary traits using real data. Naik et al [36] analyzed COVID-19 epidemics with treatment in fractional derivatives on the base of data from Pakistan and some other studies regarding COVID-19 epidemic model investigated by Ikram et al [37], Allegretti et al [38], and Joshi et al [39]. Furthermore, some respective studies associated with fractionalized models are discussed in detail; see, for instance, [40][41][42][43]; most of the studies are focused on flow problems by considering different fluids, related to fractional operators and heat transport phenomena.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

et al. 2022

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In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.

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Section: Ordinary Viscous Fluidsupporting

confidence: 83%

Section: Exact Solution Of Fluid Velocitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

et al. 2022

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“…Dynamical chaos disappears when the fractional order falls below a threshold in a fractional-order chaotic system. There have been several articles discussing the minimum effective dimension below which the system remains chaotic, [1,2,3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional fractional system with the stability condition and chaos control

Gholami

Ghaziani

Eskandari

2022

mmnsa

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A three-dimensional system is introduced in this paper and its local stability is analyzed. Our study establishes the validity and uniqueness of the linear feedback control for the proposed system and proves its existence and uniqueness. The numerical simulation algorithm described by Atanackovic and Stankovic is finally applied. The analytical results are analyzed and the dynamics of the system are explored in more detail.

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“…In the study [27], memory and hereditary traits were considered, which emphasized the advantages of the non-integer order model. Instead of a fractional model, a stochastic model comprising four human classes has been reformulated in [28]. It was shown that the solution of the proposed model existed and was unique.…”

Section: Introductionmentioning

confidence: 99%

A New Numerical Scheme for Time Fractional Diffusive SEAIR Model with Non-Linear Incidence Rate: An Application to Computational Biology

2022

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In this paper, we propose a modified fractional diffusive SEAIR epidemic model with a nonlinear incidence rate. A constructed model of fractional partial differential equations (PDEs) is more general than the corresponding model of fractional ordinary differential equations (ODEs). The Caputo fractional derivative is considered. Linear stability analysis of the disease-free equilibrium state of the epidemic model (ODEs) is presented by employing Routh–Hurwitz stability criteria. In order to solve this model, a fractional numerical scheme is proposed. The proposed scheme can be used to find conditions for obtaining positive solutions for diffusive epidemic models. The stability of the scheme is given, and convergence conditions are found for the system of the linearized diffusive fractional epidemic model. In addition to this, the deficiencies of accuracy and consistency in the nonstandard finite difference method are also underlined by comparing the results with the standard fractional scheme and the MATLAB built-in solver pdepe. The proposed scheme shows an advantage over the fractional nonstandard finite difference method in terms of accuracy. In addition, numerical results are supplied to evaluate the proposed scheme’s performance.

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Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay

Cited by 62 publications

References 24 publications

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

Three-dimensional fractional system with the stability condition and chaos control

A New Numerical Scheme for Time Fractional Diffusive SEAIR Model with Non-Linear Incidence Rate: An Application to Computational Biology

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