An epidemiological model for analysing pandemic trends of novel coronavirus transmission with optimal control

Symptomatic and asymptomatic individuals play a significant role in the transmission dynamics of novel Coronaviruses. By considering the dynamical behaviour of symptomatic and asymptomatic individuals, this study examines the temporal dynamics and optimal control of Coronavirus disease propagation using an epidemiological model. Biologically and mathematically, the well-posed epidemic problem is examined, as well as the threshold quantity with parameter sensitivity. Model parameters are quantified and their relative impact on the disease is evaluated. Additionally, the steady states are investigated to determine the model's stability and bifurcation. Using the dynamics and parameters sensitivity, we then introduce optimal control strategies for the elimination of the disease. Using real disease data, numerical simulations and model validation are performed to support theoretical findings and show the effects of control strategies.

Dynamics of non-Newtonian methanol conveying aluminium alloy over a rotating disc: consideration of variable nanoparticle radius and inter-particle spacing

The advancement of non-Newtonian nanofluid innovation is a crucial area of research for physicists, mathematicians, manufacturers, and materials scientists. In engineering and industries, the fluid velocity caused by rotating device and nanofluid has a lot of applications such as refrigerators, chips, heat ex-changers, hybrid mechanical motors, food development, and so on. Due to the tremendous usage of the non-Newtonian nanofluid, the originality of the current study is to explore the influence of nanoparticle radii and inter-particle spacing effects on the flow characteristics of Casson methanol-based aluminium alloy (AA7072) nanofluid through a rotating disc with Joule heating and magnetic dipole. The present problem is modeled in the form of partial differential equations (PDEs), and these PDEs are converted into ordinary differential equations with the help of suitable similarity transformations. The analytical solution to the current modeled problem has been obtained by using the homotopy analysis method (HAM) and numerical solutions are obtained by employing Runge-Kutta-Fehlberg method along with shooting technique. The main purpose of the present research work is to analyze the behavior of the velocity and temperature of the nanofluid for small and large radius of the aluminium alloy (AA7072) nanoparticles and inter-particle spacing. The radial and tangential velocities are enhanced due to rising ferro-hydrodynamic interaction parameter and the skin friction force for radial and tangential directions are enhanced 10.51% and 2.16% whenh= 0.5. Also, the heat transfer rate is reduced 18.71% and 16.70% whenh= 0.5% andRp= 1.5. In fact, the present results are compared with the published results and they met good agreement.

Influence of magnetic field-dependent viscosity on Casson-based nanofluid boundary layers: A comprehensive analysis using Lie group and spectral quasi-linearization method

This study examines the effects of magnetic-field-dependent (MFD) viscosity on the boundary layer flow of a non-Newtonian sodium alginate-based F e 3 O 4 nanofluid over an impermeable stretching surface. The non-Newtonian Casson and homogeneous nanofluid models are utilized to derive the governing flow and heat transfer equations. Applying Lie group transformations to dimensional partial differential equations yields nondimensional ordinary differential equations, which are then numerically solved using the spectral quasi-linearization technique. The analysis primarily focuses on the impacts of the MFD viscosity parameter, nanoparticle volume fraction of F e 3 O 4 , and magnetic parameters on the flow and heat transfer characteristics. The local skin friction and heat transfer rate behaviors influenced by viscosity changes due to the magnetic field are discussed. It is found that MFD viscosity significantly impacts flow and thermal energies, enhancing skin friction coefficients and reducing Nusselt numbers in the boundary layer region.

Numerical investigation of heat and mass transfer in three-dimensional MHD nanoliquid flow with inclined magnetization

Heat and mass transfer rate by using nanofluids is a fundamental aspect of numerous industrial processes. Its importance extends to energy efficiency, product quality, safety, and environmental responsibility, making it a key consideration for industries seeking to improve their operations, reduce costs, and meet regulatory requirements. So, the principal objective of this research is to analyze the heat and mass transfer rate for three-dimensional magneto hydrodynamic nanoliquid movement with thermal radiation and chemical reaction over the dual stretchable surface in the existence of an inclined magnetization, and viscous dissipation. The flow is rotating with constant angular speed [Formula: see text] about the axis of rotation because such flows occur in the chemical processing industry and the governing equations of motion, energy, and concentration are changed to ODEs by transformation. The complex and highly nonlinear nature of these equations makes them impractical to solve analytically so tackled numerically at MATLAB. The obtained numerical results are validated with literature and presented through graphs and tables. Increasing the Eckert number from [Formula: see text] a higher Nusselt and Sherwood number was noted for the hybrid nanofluid. By changing the angle of inclination [Formula: see text], the [Formula: see text] performance is noted at 8% for nanofluid and 33% for hybrid nanofluid. At the same time, [Formula: see text] performance of 0.5% and 2.0% are observed respectively. Additionally, as the angle of inclination increases the skin friction decreases and the chemical reaction rate increases the mass transmission rate.

Analytical solution for the dynamics and optimization of fractional Klein-Gordon equation: an application to quantum particle

Klein-Gordon equation characterizes spin-particles through neutral charge field within quantum particle. In this context, fractionalized Klein-Gordon equation is investigated for the comparative analysis of the newly presented fractional differential techniques with non-singularity among kernels. The non-singular and non-local kernels of fractional differentiations have been employed on Klein-Gordon equation for the development of governing equation. The analytical solutions of Klein-Gordon equation have been traced out by fractional techniques by means of Laplace transforms and expressed in terms of series form and gamma function. The data analysis of fractionalized Klein-Gordon equation is observed for Pearson's correlation coefficient, probable error and regression analysis. For the sake of comparative analysis of fractional techniques, 2D sketch, 3D pie chart, contour surface with projection and 3D bar sketch have been depicted on the basis of embedded parameters. Our results suggest that varying frequency has reversal trends for quantum wave and de Broglie wave.

Arrhenius kinetics driven nonlinear mixed convection flow of Casson liquid over a stretching surface in a Darcian porous medium

The non-linear mixed convective heat and mass transfer features of a non-Newtonian Casson liquid flow over a stretching surface are investigated numerically. The stretching surface is embedded in a Darcian porous medium with heat generation/absorption impacts. The fluid flow is assumed to be driven by both buoyancy and Arrhenius kinetics. The governing equations are modelled with the help of Boussinesq and Rosseland approximations. The similarity solutions of the non-dimensional equations are obtained using two numerical approaches, namely fourth fifth Runge - Kutta Fehlberg method and the shooting approach. The velocity, temperature and concentration profiles are discussed for important physical parameters through various graphical illustrations. The skin friction, the non-dimensional wall temperature, and the concentration expressions were derived and analysed. The results indicate that the increasing values of linear and nonlinear convection due to temperature, nonlinear convection due to concentration, and heat of reaction increase the dimensionless wall temperature. The dimensionless wall concentration rises with the increasing values of heat of reaction, linear and nonlinear convection due to temperature, and nonlinear convection due to concentration parameters.

Numerical study of hydrothermal and mass aspects in MHD driven Sisko-nanofluid flow including optimization analysis using response surface method

A steady, incompressible, two-dimensional Sisko-nanofluid flow towards the horizontal direction with no movement in the vertical direction is considered on a stretching/shrinking surface. The power law component (Sisko model) is incorporated under the regime of the porous medium. A magnetic impact is included coming from the MHD in the surface normal direction. In addition, thermal radiation, Brownian diffusion, and thermophoresis are involved in the governing system of equations obtained from the Navier-Stokes model in two-dimensional flow systems. The PDEs are converted into the one-dimensional system using suitable transformations and solved by Galerkin weighted residual method validated with the spectral collocation method. The optimization analysis is performed on heat transfer and skin-friction factors using response surface methodology. The impact of the parameters involved in the model has been testified and is provided in graphical forms. The outcomes indicate that for the values of the porosity factor fluctuating between [0, 2.5], the velocity profile and corresponding boundary layer thickness are lesser towards the maximum value of the parameter, and the results are opposite as the parameter approaches zero. The optimization and sensitivity analysis shows that the transport of heat sensitivity towards thermal radiation, Brownian diffusion, and thermophoresis declined whenever the Nt and Nb increased from low to high and at the medium level of thermal radiation. An increment in the Forchheimer parameter increases the sensitivity of the rate of friction factor, whereas increasing the Sisk-fluid parameter has the reverse effect. Elongation processes like those of pseudopods and bubbles make use of such models. The idea is also widely used in other sectors, such as the textile industry, glass fiber production, cooling baths, paper manufacture, and many more.

Computer Simulations of EMHD Casson Nanofluid Flow of Blood through an Irregular Stenotic Permeable Artery: Application of Koo-Kleinstreuer-Li Correlations

A novel analysis of the electromagnetohydrodynamic (EMHD) non-Newtonian nanofluid blood flow incorporating CuO and Al2O3 nanoparticles through a permeable walled diseased artery having irregular stenosis and an aneurysm is analyzed in this paper. The non-Newtonian behavior of blood flow is addressed by the Casson fluid model. The effective viscosity and thermal conductivity of nanofluids are calculated using the Koo-Kleinstreuer-Li model, which takes into account the Brownian motion of nanoparticles. The mild stenosis approximation is employed to reduce the bi-directional flow of blood to uni-directional. The blood flow is influenced by an electric field along with a magnetic field perpendicular to the blood flow. The governing mathematical equations are solved using Crank-Nicolson finite difference approach. The model has been developed and validated by comparing the current results to previously published benchmarks that are peculiar to this study. The results are utilized to investigate the impact of physical factors on momentum diffusion and heat transfer. The Nusselt number escalates with increasing CuO nanoparticle diameter and diminishing the diameter of Al2O3 nanoparticles. The relative % variation in Nusselt number enhances with Magnetic number, whereas a declining trend is obtained for the electric field parameter. The present study's findings may be helpful in the diagnosis of hemodynamic abnormalities and the fields of nano-hemodynamics, nano-pharmacology, drug delivery, tissue regeneration, wound healing, and blood purification systems.

Numerical Investigation of Heat Generation and Magnetohydrodynamic Flow of Fluid Over a Shrinking Infinite Long Cylinder Through Porous Medium

The objective of the present study is to observe the magnetohydrodynamic flow and heat transfer for the fluid flow over a shrinking cylinder of time dependent radius in a cylindrical coordinate. The flow is induced by heat generation effect and suction effect on the walls of cylinder. The governing equations modelled in terms of partial differential equation are reduced to ordinary differential equations using suitable similarity transformation variables. A numerical technique, Iterative power series has been employed using Mathematica software to tackle the problem. The two solutions are acquired for momentum and temperature profiles, which never intersect. The physical behavior of the solution has been explored in terms of parametric analysis and graphical demonstration. The skin friction and Nusselt number of practical interests has been acquired and portrayed graphically. Furthermore, for both solutions, the temperature of the fluid rises with the suction and unsteadiness parameters. We also see that when the magnetic force increases, the second solution diminishes. Finally, at a given value of the suction parameter, the two solutions for skin friction coefficient converge to a single solution.

Analysis of natural convection for a Casson-based multiwall carbon nanotube nanofluid in a partially heated wavy enclosure with a circular obstacle in the presence of thermal radiation

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Casson Sodium alginate based MWCNT nanofluid is considered in a wavy enclosure for the first time.

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Natural convection is analyzed in the presence of adiabatic/hot/cold obstacle.

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The dimensional velocities, streamlines and isotherms are discussed thoroughly.

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FEM simulations are done with thermal radiation.

Introduction

Nanofluids are considered a better alternative to conventional fluids in many industrial situations and unfolding new opportunities for various applications owing to the optical and thermal properties of additive nanosized materials.

Objectives

In this study, the thermal and hydraulic characteristics of a Casson-based (sodium alginate) multiwall carbon nanotube (MWCNT) nanofluid were computationally investigated inside a wavy square enclosure containing a circular-shaped obstacle. The square enclosure comprised two cooled vertical walls and a wavy adiabatic top wall. The central part of the bottom wall comprised a heated wavy structure, and the remaining parts exhibited a flat and adiabatic structure.

Methods

The Navier–Stokes (N–S) equations and boundary conditions were established using the non-Newtonian Casson fluid model and Rosseland thermal radiation. The present problem was numerically simulated using the Galerkin finite element method for three types of obstacles, namely, adiabatic, hot, and cold. The impacts of Casson parameter (0.001 ≤ β ≤ 0.1), Rayleigh number (10³ ≤ Ra ≤ 10⁶), nanoparticle volume fraction (0.01 ≤ φ ≤ 0.1) and radiation parameter (1 ≤ Rd ≤ 4) are analysed. A numerical code validation was performed using the available benchmark results.

Results

The characteristics of the convective radiation heat transport were clearly analyzed through the stream function and isotherm plots. For all types of obstacles, the mean Nusselt number along the heated wavy wall increased with the Casson parameter, MWCNT volume fraction, Rayleigh number, and radiation parameter. Conclusion: The heat and flow characteristics of a Casson-based MWCNT nanofluid inside a wavy square enclosure were investigated. The mean Nusselt number was higher (lower) in the presence of cold (hot) obstacles.

A new modified Kies Fréchet distribution: Applications of mortality rate of Covid-19

The purpose of this paper is to identify an effective statistical distribution for examining COVID-19 mortality rates in Canada and Netherlands in order to model the distribution of COVID-19. The modified Kies Frechet (MKIF) model is an advanced three parameter lifetime distribution that was developed by incorporating the Frechet and modified Kies families. In particular with respect to current distributions, the latest one has very versatile probability functions: increasing, decreasing, and inverted U shapes are observed for the hazard rate functions, indicating that the capability of adaptability of the model. A straight forward linear representation of PDF, moment generating functions, Probability weighted moments and hazard rate functions are among the enticing features of this novel distribution. We used three different estimation methodologies to estimate the pertinent parameters of MKIF model like least squares estimators (LSEs), maximum likelihood estimators (MLEs) and weighted least squares estimators (WLSEs). The efficiency of these estimators is assessed using a thorough Monte Carlo simulation analysis. We evaluated the newest model for a variety of data sets to examine how effectively it handled data modeling. The real implementation demonstrates that the proposed model outperforms competing models and can be selected as a superior model for developing a statistical model for COVID-19 data and other similar data sets.

A sensitivity study on carbon nanotubes significance in Darcy-Forchheimer flow towards a rotating disk by response surface methodology

The current research explores incremental effect of thermal radiation on heat transfer improvement corresponds to Darcy–Forchheimer (DF) flow of carbon nanotubes along a stretched rotating surface using RSM. Casson carbon nanotubes’ constructed model in boundary layer flow is being investigated with implications of both single-walled CNTs and multi-walled CNTs. Water and Ethylene glycol are considered a basic fluid. The heat transfer rate is scrutinized via convective condition. Outcomes are observed and evaluated for both SWCNTs and MWCNTs. The Runge–Kutta Fehlberg technique of shooting is utilized to numerically solve transformed nonlinear ordinary differential system. The output parameters of interest are presumed to depend on governing input variables. In addition, sensitivity study is incorporated. It is noted that sensitivity of SFC via SWCNT-Water becomes higher by increasing values of permeability number. Additionaly, sensitivity of SFC via SWCNT-water towards the permeability number is higher than the solid volume fraction for medium and higher permeability levels. It is also noted that sensitivity of SFC (SWCNT-Ethylene-glycol) towards volume fraction is higher for increasing permeability as well as inertia coefficient. Additionally, the sensitivity of LNN towards the Solid volume fraction is higher than the radiation and Biot number for all levels of Biot number. The findings will provide initial direction for future device manufacturing.

Efficient Numerical Algorithm for the Solution of Eight Order Boundary Value Problems by Haar Wavelet Method

In this paper, the Haar technique is applied to both nonlinear and linear eight-order boundary value problems. The eight-order derivative in the boundary value problem is approximated using Haar functions in this technique and the integration process is used to obtain the expression of the lower order derivative and the approximate solution of the unknown function. For the verification of validation and convergence of the proposed technique, three linear and two nonlinear examples are taken from the literature. The results are also compared with other methods available in the literature. Maximum absolute and root mean square errors at various collocation and Gauss points are contrasted with the exact solution. The convergence rate is also measured, which is almost equivalent to 2, using different numbers of collocation points.

Stability analysis of fractional nabla difference COVID-19 model

Microorganisms lives with us in our environment, touching infectious material on the surfaces by hand-mouth which causes infectious diseases and some of these diseases are rapidly spreading from person to person. These days the world facing COVID-19 pandemic disease. This article concerned with existence of results and stability analysis for a nabla discrete ABC-fractional order COVID-19. The nabla discrete ABC-fractional operator as more general and applicable in modeling of dynamical problems due to its non-singular kernel. For the existence and uniqueness theorems and Hyers-Ulam stability, we need to suppose some conditions which will play important role in the proof of our main results. At the end, an expressive example is given to provide an application for the nabla discrete ABC-fractional order COVID-19 model.

On the analysis of number of deaths due to Covid -19 outbreak data using a new class of distributions

In this article, we develop a generator to suggest a generalization of the Gumbel type-II model known as generalized log-exponential transformation of Gumbel Type-II (GLET-GTII), which extends a more flexible model for modeling life data. Owing to basic transformation containing an extra parameter, every existing lifetime model can be made more flexible with suggested development. Some specific statistical attributes of the GLET-GTII are investigated, such as quantiles, uncertainty measures, survival function, moments, reliability, and hazard function etc. We describe two methods of parametric estimations of GLET-GTII discussed by using maximum likelihood estimators and Bayesian paradigm. The Monte Carlo simulation analysis shows that estimators are consistent. Two real life implementations are performed to scrutinize the suitability of our current strategy. These real life data is related to Infectious diseases (COVID-19). These applications identify that by using the current approach, our proposed model outperforms than other well known existing models available in the literature.

Numerical study of heat generating γ Al 2 O 3 - H 2 O nanofluid inside a square cavity with multiple obstacles of different shapes

A numerical research on uniformly heat generating γ Al₂O₃–H₂O nanofluid filled square cavity with multiple obstacles of different shapes is carried out. The cavity is assumed to be heated at bottom and cooled by vertical walls with linearly varying temperature. An adiabatic condition is assumed at the top of the cavity. Circular, square and triangular shaped obstacles are considered. The mathematical model has been solved using Galerkin finite element method. Results are presented for streamlines, isotherms, local and mean Nusselt numbers. Multiple rotating cells are observed in the streamlines. It is found that the local and mean Nusselt numbers increase with nanoparticle volume fraction and higher heat transfer is achieved in the cavity with triangular obstacles.

Fractional order mathematical modeling of COVID-19 transmission

In this article, the mathematical model with different compartments for the transmission dynamics of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding the existence of at least one solution through fixed point results are derived. Then for the concerned approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is utilized. Initially, we simulate the results by using some available data for different fractional-order to show the appropriateness of the proposed method. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

Riga - Plate flow of γ Al2O3-water/ethylene glycol with effective Prandtl number impacts

In many industrial processes, the cooling process can be improved by varying the flow geometry or changing the additives in the working fluid. The present work concentrates on the flow of γ Al₂O₃ –Water/Ethylene Glycol over a Gailitis and Lielausis device with an effective Prandtl number for the first time. The thermal transport aspects of electro-MHD boundary layer flow of γ Al₂O₃ nanofluids over a stretchable Riga plate are studied in two dimensions. The wall parallel Lorentz force is produced due to an external electric field by Riga plate to control the nanofluid flow. Mathematical models are developed with an effective Prandtl number. The no-slip and the prescribed surface temperature boundary conditions are assumed. Results are discussed using numerical results obtained by fourth order RK method with shooting technique. Special case analytical solutions are presented for both momentum and energy equations. The increasing behaviour in velocity profile and decreasing behaviours in temperature, skin friction and Nusselt number are observed with increasing modified Hartmann number. The higher modified Hartmann number leads to a sudden enhancement in the velocity profile of the nanofluid in the presence of effective Pr near the riga plate wall.