A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach

Botmart, Thongchai; Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Weera, Wajaree; Sadat, R.; Ali, Mohamed R.

doi:10.3390/fractalfract6030139

Cited by 21 publications

(14 citation statements)

References 31 publications

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“…Recently, stochastic solvers have been presented to solve the fractional dynamical models. Few of them are dynamical nonlinear susceptible infected and quarantine differential model [55], immune-chemotherapeutic treatment for breast cancer [56], nonlinear prey-predator system [57], SIDARTHE COVID-19 pandemic differential model [58], Bagley-Torvik mathematical model [59] and seventh order singular system [60]. It is found that the time FO derivatives have been applied to different conditions in various applications.…”

Section: Novel Stochastic Solvers Featuresmentioning

confidence: 99%

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

Botmart¹,

Hiader²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

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The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system (VHDNS) along with the numerical treatment of artificial neural networks (ANNs) techniques supported by Levenberg-Marquardt backpropagation (LMQBP), known as ANNs-LMQBP. This mechanism is physically appropriate, where the number of infected people is increasing along with the limited health services. Furthermore, the biological effects have fading memories and exhibit transition behavior. Initially, the model is developed by considering the two and three categories for the humans and the vector species. The VHDNS is constructed with five classes, susceptible humans S h (t), infected humans I h (t), recovered humans R h (t), infected vectors I v (t) , and susceptible vector S v (t) based system of the fractional-order nonlinear ordinary differential equations. To solve the number of variations of the VHDNS, the numerical simulations are performed using the stochastic ANNs-LMQBP. The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training, verifying, and testing data to decrease the mean square error (MSE). An extensive analysis is provided using the correlation studies, MSE, error histograms (EHs), state transitions (STs), and regression to observe the accuracy, efficiency, expertise, and aptitude of the computing ANNs-LMQBP.

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Section: Novel Stochastic Solvers Featuresmentioning

confidence: 99%

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

Botmart¹,

Hiader²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

Self Cite

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“…The stochastic solvers have been tested through the local and global operator performances to solve a few nonlinear, singular, and complicated differential models. Few applications of the stochastic applications are COVID-19 systems [16,17], fractional order models [18,19], functional order system [20], periodic differential system [21], third kind of nonlinear singular system [22] delay singular model [23], dynamics of the food chain models [24], and singular explosion theory models [25].…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

Weera¹,

Zamart²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

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The motive of these investigations is to provide the importance and significance of the fractional order (FO) derivatives in the nonlinear environmental and economic (NEE) model, i.e., FO-NEE model. The dynamics of the NEE model achieves more precise by using the form of the FO derivative. The investigations through the non-integer and nonlinear mathematical form to define the FO-NEE model are also provided in this study. The composition of the FO-NEE model is classified into three classes, execution cost of control, system competence of industrial elements and a new diagnostics technical exclusion cost. The mathematical FO-NEE system is numerically studied by using the artificial neural networks (ANNs) along with the Levenberg-Marquardt backpropagation method (ANNs-LMBM). Three different cases using the FO derivative have been examined to present the numerical performances of the FO-NEE model. The data is selected to solve the mathematical FO-NEE system is executed as 70% for training and 15% for both testing and certification. The exactness of the proposed ANNs-LMBM is observed through the comparison of the obtained and the Adams-Bashforth-Moulton database results. To ratify the aptitude, validity, constancy, exactness, and competence of the ANNs-LMBM, the numerical replications using the state transitions, regression, correlation, error histograms and mean square error are also described.

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“…Furthermore, ANNs are important to forecast the findings of theoretical and numerical approximation studies of nanofluidic models (Sheikholeslami et al, 2019c;Sabir et al, 2022;Zuhra et al, 2022). Levenberg-Marquardt backpropagation neural network has been applied for the computational purpose of the nanofluid model (Vakili et al, 2016;Shah et al, 2021b;Shoaib et al, 2021;Umar et al, 2021;Botmart et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

MHD williamson nanofluid flow in the rheology of thermal radiation, joule heating, and chemical reaction using the Levenberg–Marquardt neural network algorithm

et al. 2022

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Various studies have been conducted on the topic of predicting the thermal conductivity of nanofluids. Here, the thermal conductivity of nanofluids is determined using artificial neural networks since this approach is rapid and accurate, as well as cost-effective. To forecast the thermal conductivity of magnetohydrodynamic Williamson nanofluids flow through a vertical sheet, a feed-forward neural network with various numbers of neurons has been evaluated, and the best network based on the performance is selected. The fluid model incorporates the effects of Joule heating, heat generation absorption, thermal radiation, and a chemical reaction (MHD-WNF-HGA). A combination of heat radiation and reactive species improves the energy and solute profiles. The magnetic Reynolds number is assumed to be so small; therefore, the generated magnetic field has no effect. A postulate of similarity variables is used to convert the physical model in the form of nonlinear partial differential equations to an ordinary differential equation system. A supervised Levenberg–Marquardt backpropagation algorithm possesses a multilayer perceptron that is used for training the network, which is one of the top algorithms in machine learning. The bvp4c numerical technique is adopted to build the datasets for the construction of continuous neural network mapping. Flow, energy, and concentration profiles of the fluidic flow are constructed by adjusting several physical quantities such as the Williamson parameter, thermal radiation parameter, magnetic parameter, Eckert number, Darcy number, Brownian motion, and thermophoresis parameter. Analytical techniques such as error histogram graphs and regression-based statistical graphs are used to examine the accuracy of a suggested method. It has been found that the Levenberg–Marquardt backpropagation neural network mappings’ derivation, convergence, authentication, and consistency have been proven. Furthermore, thermal radiation assists the energy distribution to increase smoothly. Fluid velocity drops with the Williamson parameter, whereas thermophoresis impact enhances the strength of the nanofluid density.

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A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach

Cited by 21 publications

References 31 publications

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

MHD williamson nanofluid flow in the rheology of thermal radiation, joule heating, and chemical reaction using the Levenberg–Marquardt neural network algorithm

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