A Study on the Transmission Dynamics of the Omicron Variant of COVID-19 Using Nonlinear Mathematical Models

This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.

An Efficient Technique for One-Dimensional Fractional Diffusion EquationModel for Cancer Tumor

This study intends to examine the analytical solutions to the resulting one-dimensional differential equation of acancer tumor model in the frame of time-fractional order with the Caputo-fractional operator employing a highlyefficient methodology called the q-homotopy analysis transform method.So,the preferred approach effectivelyfound the analytic series solution of the proposed model.The procured outcomes of the present frameworkdemonstrated that this method is authentic for obtaining solutions to a time-fractional-order cancer model.Theresults achieved graphically specify that the concerned paradigm is dependent on arbitrary order and parametersand also disclose the competence of the proposed algorithm.

Mathematical Analysis of Novel Coronavirus (2019-nCov) Delay Pandemic Model

In this manuscript,the mathematical analysis of corona virus model with time delay effect is studied.Mathematical modelling of infectious diseases has substantial role in the different disciplines such as biological,engineering,physical,social,behavioural problems and many more.Most of infectious diseases are dreadful such as HIV/AIDS,Hepatitis and 2019-nCov.Unfortunately,due to the non-availability of vaccine for 2019-nCov around the world,the delay factors like,social distancing,quarantine,travel restrictions,holidays extension,hospitalization and isolation are used as key tools to control the pandemic of 2019-nCov.We have analysed the reproduction number𝐑𝐑𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧of delayed model.Two key strategies from the reproduction number of 2019-nCov model,may be followed,according to the nature of the disease as if it is diminished or present in the community.The more delaying tactics eventually,led to the control of pandemic.Local and global stability of 2019-nCov model is presented for the strategies.We have also investigated the effect of delay factor on reproduction number𝐑R_(nCov).Finally,some very useful numerical results are presented to support the theoretical analysis of the model.

A New Metaheuristic Optimization Algorithms for Brushless Direct Current Wheel Motor Design Problem

The Equilibrium Optimizer(EO),Grey Wolf Optimizer(GWO),and Whale Optimizer(WO)algorithms are being recently developed for engineering optimization problems.In this paper,the EO,GWO,and WO algorithms are applied individually for a brushless direct current(BLDC)design optimization problem.The EO algorithm is inspired by the models utilized to find the system’s dynamic state and equilibrium state.The GWO and WO algorithms are inspired by the hunting behavior of the wolf and the whale,respectively.The primary purpose of any optimization technique is to find the optimal configuration by maximizing motor efficiency and/or minimizing the total mass.Therefore,two objective functions are being used to achieve these objectives.The first refers to a design with high power output and efficiency.The second is a constraint imposed by the reality that the motor is built into the wheel of the vehicle and,therefore,a lightweight is needed.The EO,GWO,and WOA algorithms are then utilized to optimize the BLDC motor’s design variables to minimize the motor’s total mass or maximize the motor efficiency by simultaneously satisfying the six inequality constraints.The simulation is carried out using MATLAB simulation software,and the simulation results prove the dominance of the proposed algorithms.This paper also suggests an efficient method from the proposed three methods for the BLDC motor design optimization problem.

A Structure Preserving Numerical Method for Solution of Stochastic Epidemic Model of Smoking Dynamics

In this manuscript,we consider a stochastic smoking epidemic model from behavioural sciences.Also,we develop a structure preserving numerical method to describe the dynamics of stochastic smoking epidemic model in a human population.The structural properties of a physical system include positivity,boundedness and dynamical consistency.These properties play a vital role in non-linear dynamics.The solution for nonlinear stochastic models necessitates the conservation of these properties.Unfortunately,the aforementioned properties of the model have not been restored in the existing stochastic methods.Therefore,it is essential to construct a structure preserving numerical method for a reliable analysis of stochastic smoking model.The usual explicit stochastic numerical methods are time-dependent and violate most of the structural properties.In this work,we have developed the implicitly driven explicit method for the solution of stochastic smoking model.It is also proved that the newly developed method sustains all the aforementioned properties of the system.Finally,the convergence analysis of the newly developed method and graphical illustrations are presented.

Design of Computer Methods for the Solution of Cervical Cancer Epidemic Model

Nonlinear modelling has a significant role in different disciplines of sciences such as behavioral,social,physical and biological sciences.The structural properties are also needed for such types of disciplines,as dynamical consistency,positivity and boundedness are the major requirements of the models in these fields.One more thing,this type of nonlinear model has no explicit solutions.For the sake of comparison its computation will be done by using different computational techniques.Regrettably,the aforementioned structural properties have not been restored in the existing computational techniques in literature.Therefore,the construction of structural preserving computational techniques are needed.The nonlinearmodel for cervical cancer is constructed by parametric perturbation technique.Well-known computer methods are considered for the computation of cervical cancer dynamics.The well-known existing methods in literature are Euler Maruyama,Euler and Runge Kutta.Nonstandard finite difference method or Implicitly driven explicit method is first time considered for aforesaid model under the assumptions given byMickens in a stochastic way.Unfortunately,the aforementioned existing methods did not reinstate structural properties of cervical cancer dynamics in the human population.Our plannedmethod is structural preserving and a powerful tool for all nonlinear models of biomedical engineering problems.We have verified that existing computational methods do not preserve dynamical properties.But,the implicitly driven explicit method is a good device for dynamical properties.In the support of assertions,convergence analysis of implicitly driven explicit method is presented.

Al_(2)O_(3) andγAl_(2)O_(3) Nanomaterials Based Nanofluid Models with Surface Diffusion:Applications for Thermal Performance in Multiple Engineering Systems and Industries

Thermal transport investigation in colloidal suspensions is taking a significant research direction.The applications of these fluids are found in various industries,engineering,aerodynamics,mechanical engineering and medical sciences etc.A huge amount of thermal transport is essential in the operation of various industrial production processes.It is a fact that conventional liquids have lower thermal transport characteristics as compared to colloidal suspensions.The colloidal suspensions have high thermal performance due to the thermophysical attributes of the nanoparticles and the host liquid.Therefore,researchers focused on the analysis of the heat transport in nanofluids under diverse circumstances.As such,the colloidal analysis of H_(2)O composed byγAl_(2)O_(3)and Al_(2)O_(3)is conducted over an elastic cylinder.The governing flow models ofγAl_(2)O_(3)/H_(2)O and Al_(2)O_(3)/H_(2)O is reduced in the dimensionless form by adopting the described similarity transforms.The colloidal models are handled by implementing the suitable numerical technique and provided the results for the velocity,temperature and local thermal performance rate against the multiple flow parameters.From the presented results,it is shown that the velocity of Al_(2)O_(3)–H_(2)O increases promptly against a high Reynolds number and it decreases for high-volume fraction.The significant contribution of the volumetric fraction is examined for thermal enhancement of nanofluids.The temperature of Al_(2)O_(3)–H_(2)O andγAl_(2)O_(3)–H_(2)O significantly increases against a higherϕ.Most importantly,the analysis shows thatγAl_(2)O_(3)–H_(2)O has a high local thermal performance rate compared to Al_(2)O_(3)–H_(2)O.Therefore,it is concluded thatγAl_(2)O_(3)–H_(2)O is a better heat transfer fluid and is suitable for industrial and technological uses.

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19in Nigeria Using Atangana-Baleanu Operator

We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.

Heat Transfer in MHD Flow of Maxwell Fluid via Fractional Cattaneo-Friedrich Model:A Finite Difference Approach

The idea of fractional derivatives is applied to several problems of viscoelastic fluid.However,most of these problems(fluid problems),were studied analytically using different integral transform techniques,as most of these problems are linear.The idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential equations.Most importantly,in the nonlinear problems,either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems(without developing the fractional model even using artificial replacement)are solved.These problems were mostly solved for steady-state fluid problems.In the present article,studied unsteady nonlinear non-Newtonian fluid problem(Cattaneo-Friedrich Maxwell(CFM)model)and the fractional model are developed starting from the fractional constitutive equations to the fractional governing equations;in other words,the artificial replacement of the classical derivatives with fractional derivatives is not done,but in details,the fractional problem is modeled from the fractional constitutive equations.More exactly two-dimensional magnetic resistive flow in a porous medium of fractional Maxwell fluid(FMF)over an inclined plate with variable velocity and the temperature is studied.The Caputo time-fractional derivative model(CFM)is used in the governing equations.The proposed model is numerically solved via finite difference method(FDM)along with L1-scheme for discretization.The numerical results are presented in various figures.These results indicated that the fractional parameters significantly affect the temperature and velocity fields.It is noticed that the temperature field increased with an increase in the fractional parameter.Whereas,the effect of fractional parameters is opposite on the velocity field near the plate.However,this trend became like that of the temperature profile,away from the plate.Moreover,the velocity field retarded with strengthening in the magnetic parameter due to enhancement in Lorentz force.However,this effect reverses in the case of the temperature profile.

Computational Analysis of the Effect of Nano Particle Material Motion on Mixed Convection Flow in the Presence of Heat Generation and Absorption

The present study is concerned with the physical behavior of the combined effect of nano particle material motion and heat generation/absorption due to the effect of different parameters involved in prescribed flow model.The formulation of the flow model is based on basic universal equations of conservation of momentum,energy and mass.The prescribed flow model is converted to non-dimensional form by using suitable scaling.The obtained transformed equations are solved numerically by using finite difference scheme.For the analysis of above said behavior the computed numerical data for fluid velocity,temperature profile,and mass concentration for several constraints that is mixed convection parameterλt,modified mixed convection parameterλc,Prandtl number Pr,heat generation/absorption parameterδ,Schmidt number Sc,thermophoresis parameter Nt,and thermophoretic coefficient k are sketched in graphical form.Numerical results for skin friction,heat transfer rate and the mass transfer rate are tabulated for various emerging physical parameters.It is reported that in enhancement in heat,generation boosts up the fluid temperature at some positions of the surface of the sphere.As heat absorption parameter is decreased temperature field increases at position X=π/4 on the other hand,no alteration at other considered circumferential positions is noticed.

Temporal Stability Analysis of Magnetized Hybrid Nanofluid Propagating through an Unsteady Shrinking Sheet: Partial Slip Conditions

The unsteady magnetohydrodynamic(MHD)flow on a horizontal preamble surface with hybrid nanoparticles in the presence of the first order velocity and thermal slip conditions are investigated.Alumina(Al_(2)O_(3))and copper(Cu)are considered as hybrid nanoparticles that have been dispersed in water in order to make hybrid nanofluid(Cu-Al_(2)O_(3)/water).The system of similarity equations is derived from the system of partial differential equations(PDEs)by using variables of similarity,and their solutions are gotten with shooting method in the Maple software.In certain ranges of unsteadiness and magnetic parameters,the presence of dual solutions can be found.Further,it is examined that layer separation is deferred due to the effect of the hybrid nanoparticles.Moreover,the capacity of the thermal enhancement of Cu-Al_(2)O_(3)/water hybrid nanofluid is higher as compared to Al_(2)O_(3)/water based nanofluid and enhancements inCu are caused to rise the fluid temperature in both solutions.In the last,solutions stability analyzes were also carried out and the first solution was found to be stable.

Second Law Analysis of Magneto Radiative GO-MoS_(2)/H_(2)O–(CH_(2)OH)_(2) Hybrid Nanofluid

Entropy Generation Optimization(EGO)attained huge interest of scientists and researchers due to its numerous applications comprised in mechanical engineering,air conditioners,heat engines,thermal machines,heat exchange,refrigerators,heat pumps and substance mixing etc.Therefore,the study of radiative hybrid nanofluid(GO-MoS_(2)/C_(2)H_(6)O_(2)–H_(2)O)and the conventional nanofluid(MoS_(2)/C_(2)H_(6)O_(2)–H_(2)O)is conducted in the presence of Lorentz forces.The flow configuration is modeled between the parallel rotating plates in which the lower plate is permeable.The models which govern the flow in rotating system are solved numerically over the domain of interest and furnished the results for the temperature,entropy generation and thermophysical characteristics of the hybrid as well as conventional nanofluids,respectively.It is examined that the thermal profile intensifies against stronger thermal radiations and magnetic field.The surface of the plate is heated due to the imposed thermal radiations and magnetic field which cause the increment in the temperature.It is also observed that the temperature declines against more rotating plates.Further,the entropy production increases for more dissipative effects and declines against more magnetized fluid.Thermal conductivities of the hybrid nanofluid enhances promptly in comparison with regular liquid therefore,under consideration hybrid nanofluid is reliable for the heat transfer.Moreover,dominating thermal transport is perceived for the hybrid nanofluid which showed that hybrid suspension GO-MoS_(2)/C_(2)H_(6)O_(2)–H_(2)O is better for industrial,engineering and technological uses.

Numerical Analysis of Novel Coronavirus (2019-nCov) Pandemic Model with Advection

Recently,the world is facing the terror of the novel corona-virus,termed as COVID-19.Various health institutes and researchers are continuously striving to control this pandemic.In this article,the SEIAR(susceptible,exposed,infected,symptomatically infected,asymptomatically infected and recovered)infection model of COVID-19 with a constant rate of advection is studied for the disease propagation.A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system.The continuous model is transposed into a discrete numerical model by discretizing the domains,finitely.To analyze the disease dynamics,a structure preserving non-standard finite difference scheme is designed.Two steady states of the continuous system are described i.e.,virus free steady state and virus existing steady state.Graphical results show that both the steady states of the numerical design coincide with the fixed points of the continuous SEIAR model.Positivity of the state variables is ensured by applying the M-matrix theory.A result for the positivity property is established.For the proposed numerical design,two different types of the stability are investigated.Nonlinear stability and linear stability for the projected scheme is examined by applying some standard results.Von Neuman stability test is applied to ensure linear stability.The reproductive number is described and its pivotal role in stability analysis is also discussed.Consistency and convergence of the numerical model is also studied.Numerical graphs are presented via computer simulations to prove the worth and efficiency of the quarantine factor is explored graphically,which is helpful in controlling the disease dynamics.In the end,the conclusion of the study is also rendered.

Computational Analysis of the Oscillatory Mixed Convection Flow along a Horizontal Circular Cylinder in Thermally Stratified Medium

The present work emphasizes the significance of oscillatory mixed convection stratified fluid and heat transfer characteristics at different stations of non-conducting horizontally circular cylinder in the presence of thermally stratified medium.To remove the difficulties in illustrating the coupled PDE’s,the finite-difference scheme with efficient primitive-variable formulation is proposed to transform dimensionless equations.The numerical simulations of coupled non-dimensional equations are computed in terms velocity of fluid,temperature and magnetic field which are computed to examine the fluctuating components of skin friction,heat transfer and current density for various emerging parameters.The governing parameters namely,thermally stratification parameter𝑆𝑆𝑡𝑡,mixed-convection parameter𝜆𝜆,Prandtl number Pr,magnetic force parameter𝜉𝜉and magnetic-Prandtl number𝛾𝛾are displayed graphically at selected values for velocity and heat transfer mechanism.It is computed that heat transfer attains maximum amplitude and good variations in the presence of thermally stratified parameter at each position𝛼𝛼=𝜋𝜋6⁄,𝛼𝛼=𝜋𝜋3⁄and𝛼𝛼=𝜋𝜋around the surface of non-conducting horizontally cylinder.The velocity of fluid attains certain height at station𝛼𝛼=𝜋𝜋6⁄for higher value of stratification parameter.It is also found that the temperature gradient decreases with stratification parameter𝑆𝑆𝑡𝑡,but it increases after a certain distance𝑌𝑌from the cylinder.The novelty of the current work is that due to non-conducting phenomena the magnetic effects are strongly observed far from the surface but exact at the surface are zero for each position.

Structure Preserving Algorithm for Fractional Order Mathematical Model of COVID-19

In this article,a brief biological structure and some basic properties of COVID-19 are described.A classical integer order model is modified and converted into a fractional order model withξas order of the fractional derivative.Moreover,a valued structure preserving the numerical design,coined as Grunwald–Letnikov non-standard finite difference scheme,is developed for the fractional COVID-19 model.Taking into account the importance of the positivity and boundedness of the state variables,some productive results have been proved to ensure these essential features.Stability of the model at a corona free and a corona existing equilibrium points is investigated on the basis of Eigen values.The Routh–Hurwitz criterion is applied for the local stability analysis.An appropriate example with fitted and estimated set of parametric values is presented for the simulations.Graphical solutions are displayed for the chosen values ofξ(fractional order of the derivatives).The role of quarantined policy is also determined gradually to highlight its significance and relevancy in controlling infectious diseases.In the end,outcomes of the study are presented.

BHGSO:Binary Hunger Games Search Optimization Algorithm for Feature Selection Problem

In machine learning and data mining,feature selection(FS)is a traditional and complicated optimization problem.Since the run time increases exponentially,FS is treated as an NP-hard problem.The researcher’s effort to build a new FS solution was inspired by the ongoing need for an efficient FS framework and the success rates of swarming outcomes in different optimization scenarios.This paper presents two binary variants of a Hunger Games Search Optimization(HGSO)algorithm based on V-and S-shaped transfer functions within a wrapper FS model for choosing the best features from a large dataset.The proposed technique transforms the continuous HGSO into a binary variant using V-and S-shaped transfer functions(BHGSO-V and BHGSO-S).To validate the accuracy,16 famous UCI datasets are considered and compared with different state-of-the-art metaheuristic binary algorithms.The findings demonstrate that BHGSO-V achieves better performance in terms of the selected number of features,classification accuracy,run time,and fitness values than other state-of-the-art algorithms.The results demonstrate that the BHGSO-V algorithm can reduce dimensionality and choose the most helpful features for classification problems.The proposed BHGSO-V achieves 95%average classification accuracy for most of the datasets,and run time is less than 5 sec.for low and medium dimensional datasets and less than 10 sec for high dimensional datasets.

Is Social Distancing, and Quarantine Effective in Restricting COVID-19 Outbreak? Statistical Evidences from Wuhan, China

The flow of novel coronavirus(COVID-19)has affected almost every aspect of human life around the globe.Being the emerging ground and early sufferer of the virus,Wuhan city-data remains a case of multifold significance.Further,it is of notable importance to explore the impact of unique and unprecedented public health response of Chinese authorities—the extreme lockdown of the city.In this research,we investigate the statistical nature of the viral transmission concerning social distancing,extreme quarantine,and robust lockdown interventions.We observed highly convincing and statistically significant evidences in favor of quarantine and social distancing approaches.These findings might help countries,now facing,or likely to face the wave of the virus.We analyzed Wuhan-based data of“number of deaths”and“confirmed cases,”extracted from China CDC weekly database,dated from February 13,2020,to March 24,2020.To estimate the underlying group structure,the assembled data is further subdivided into three blocks,each consists of two weeks.Thus,the complete data set is studied in three phases,such as,phase 1(Ph 1)=February 13,2020,to February 26,2020;phase 2(Ph 2)=February 27,2020 to March 11,2020;and phase 3(Ph 3)=March 12,2020 to March 24,2020.We observed the overall median proportion of deaths in those six weeks remained 0.0127.This estimate is highly influenced by Ph1,when the early flaws of weak health response were still prevalent.Over the time,we witnessed a median decline of 92.12%in the death proportions.Moreover,a non-parametric version of the variability analysis of death data,estimated that the average rank of reported proportions in Ph 3 remained 7,which was 20.5 in Ph 2,and stayed 34.5 in the first phase.Similar patterns were observed,when studying the confirmed cases data.We estimated the overall median of the proportion of confirmed cases in Wuhan as 0.0041,which again,is highly inclined towards Ph 1 and Ph 2.We also witnessed minimum average rank proportions for Ph 3,such as 7,which was noticeably lower than Ph 2,21.71,and Ph 1, 32.29. Moreover, the varying degree of clustering indicates that the effectivenessof quarantine based policies is time-dependent. In general, the declinein coronavirus transmission in Wuhan significantly coincides with the lockdown.

An Unsteady Oscillatory Flow of Generalized Casson Fluid with Heat and Mass Transfer:A Comparative Fractional Model

It is of high interest to study laminar flow with mass and heat transfer phenomena that occur in a viscoelastic fluid taken over a vertical plate due to its importance in many technological processes and its increased industrial applications.Because of its wide range of applications,this study aims at evaluating the solutions corresponding to Casson fluids’oscillating flow using fractional-derivatives.As it has a combined mass-heat transfer effect,we considered the fluid flow upon an oscillatory infinite vertical-plate.Furthermore,we used two new fractional approaches of fractional derivatives,named AB(Atangana–Baleanu)and CF(Caputo–Fabrizio),on dimensionless governing equations and then we compared their results.The Laplace transformation technique is used to get the most accurate solutions of oscillating motion of any generalized Casson fluid because of the Cosine oscillation passed over the infinite vertical-plate.We obtained and analyzed the distribution of concentration,expressions for the velocity-field and the temperature graphically,using various parameters of interest.We also analyzed the Nusselt number and the skin friction due to their important engineering usage.

A New Idea of Fractal-Fractional Derivative with Power Law Kernel for Free Convection Heat Transfer in a Channel Flow between Two Static Upright Parallel Plates

Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.

Comparative Thermal Performance in SiO_(2)–H_(2)O and (MoS_(2)–SiO_(2))–H_(2)O Over a Curved Stretching Semi-Infinite Region: A Numerical Investigation

The investigation of Thermal performance in nanofluids and hybrid nanofluids over a curved stretching infinite region strengthens its roots in engineering and industry.Therefore,the comparative thermal analysis in SiO_(2)–H_(2)O and(MoS_(2)–SiO_(2))–H_(2)O is conducted over curved stretching surface.The model is reduced in the dimensional version via similarity transformation and then treated numerically.The velocity and thermal behavior for both the fluids is decorated against the preeminent parameters.From the analysis,it is examined that the motion of under consideration fluids declines against Fr and
.The thermal performance enhances for higher volumetric fraction and
.Further,it is noticed that thermal performance prevailed in(MoS_(2)–SiO_(2))–H_(2)O throughout the analysis.Therefore,(MoS_(2)–SiO_(2))–H_(2)O is better for industrial and engineering uses where high heat transfer is required to accomplished different processes of production.