Boundedness and Positivity Preserving Numerical Analysis of a Fuzzy-Parameterized Delayed Model for Foot and Mouth Disease Dynamics

Foot-and-mouth disease(FMD)is a viral disease that affects cloven-hoofed animals including cattle,pigs,and sheep,hence causing export bans among others,causing high economic losses due to reduced productivity.The global effect of FMD is most felt where livestock rearing forms an important source of income.It is therefore important to understand the modes of transmission of FMD to control its spread and prevent its occurrence.This work intends to address these dynamics by including the efficacy of active migrant animals transporting the disease from one area to another in a fuzzy mathematical modeling framework.Historical models of epidemics are determinable with a set of deterministic parameters and this does not reflect on real-life scenarios as observed in FMD.Fuzzy theory is used in this model as it permits the inclusion of uncertainties in the model;this makes the model more of a reality regarding disease transmission.A time lag,in this case,denotes the incubation period and other time-related factors affecting the spread of FMD and,therefore,is added to the current model for FMD.To that purpose,the analysis of steady states and the basic reproduction number are performed and,in addition,the stability checks are conveyed in the fuzzy environment.For the numerical solution of the model,we derive the Forward Euler Method and the fuzzy delayed non-standard finite difference(FDNSFD)method.Analytical studies of the FDNSFD scheme are performed for convergence,non-negativity,boundedness,and consistency analysis of the numerical projection to guarantee that the numerical model is an accurate discretization of the continuous dynamics of FMD transmission over time.In the following simulation study,we show that the FDNSFD method preserves the characteristics of the constant model and still works if relatively large time steps are employed;this is a bonus over the normal finite difference technique.The study shows how valuable it is to adopt fuzzy theory and time delays when simulating the transmission of the epidemic,especially for such diseases as FMD where uncertainty and migration have a defining role in transmission.This approach gives more sound and flexible grounds for analyzing and controlling the outbreak of FMD in various situations.

Experimental and computational study of annealed nickel sulfide quantum dots for catalytic and antibacterial activity

This research investigates the hydrothermal synthesis and annealing duration effects on nickel sulfide(NiS_(2) quantum dots(QDs)for catalytic decolorization of methylene blue(MB)dye and antimicrobial efficacy.QD size increased with longer annealing,reducing catalytic activity.UV–vis,XRD,TEM,and FTIR analyses probed optical structural,morphological,and vibrational features.XRD confirmed NiS2's anorthic structure,with crystallite size growing from 6.53 to 7.81 nm during extended annealing.UV–Vis exhibited a bathochromic shift,reflecting reduced band gap energy(Eg)in NiS_(2).TEM revealed NiS_(2)QD formation,with agglomerated QD average size increasing from 7.13 to 9.65 nm with prolonged annealing.Pure NiS_(2) showed significant MB decolorization(89.85%)in acidic conditions.Annealed NiS_(2) QDs demonstrated notable antibacterial activity,yielding a 6.15mm inhibition zone against Escherichia coli(E.coli)compared to Ciprofloxacin.First-principles computation supported a robust interaction between MB and NiS_(2),evidenced by obtained adsorption energies.This study highlights the nuanced relationship between annealing duration,structural changes,and functional properties in NiS_(2)QDs,emphasizing their potential applications in catalysis and antibacterial interventions.

Influence of different cultivars of Phoenix dactylifera L-date fruits on blood clotting and wound healing

Objective: To investigate different types of dates and medical properties of influencing blood clotting and wound healing in an animal model. Methods: Three different cultivars of dates(Ajwa, Khalas, and Fardh) were examined in-vivo, for blood clotting and wound healing using CD1 mice of both sexes. Study of toxicity to animals was performed accordingly prior to further investigations. The ethanolic extracts were given orally to animals as a constituent in their daily water. Blood samples were obtained from the mice inferior vena cava to carry out the prothrombin time(PT) assay using the manual method and confirmed using a semi-automated machine. The bleeding time(BT) assay was performed using the cutting technique. In the wound healing analysis, a small cut(5-10 mm) in the skin overlying the thigh was conducted in all mice under anesthesia. The diameter of the cut and healing status were measured on a daily basis throughout the time of the experiment using a roller. Results: Ajwa was able to elevate both PT and BT(P<0.05), significantly in a time-dependent manner followed by Khalas date(P<0.05). The results of PT and BT of Fardh date were found to be very close to those of the control group(P<0.05). Despite its activity as an anticoagulant, Khalas date showed a potential property to enhance wound healing in contrast to other dates and the control groups in this study. Conclusions: Omani Khalas date fruit has both antithrombotic as well as wound healing properties. The results open a new gate with these fruits for exploring the potential component(s) that may play an important role in antithrombotic as well as wound healing process.

Computational Analysis of Heat and Mass Transfer in Magnetized Darcy-Forchheimer Hybrid Nanofluid Flow with Porous Medium and Slip Effects

A computational analysis of magnetized hybrid Darcy-Forchheimer nanofluid flow across a flat surface is presented in this work.For the study of heat and mass transfer aspects viscous dissipation,activation energy,Joule heating,thermal radiation,and heat generation effects are considered.The suspension of nanoparticles singlewalled carbon nanotubes(SWCNTs)and multi-walled carbon nanotubes(MWCNTs)are created by hybrid nanofluids.However,single-walled carbon nanotubes(SWCNTs)produce nanofluids,with water acting as conventional fluid,respectively.Nonlinear partial differential equations(PDEs)that describe the ultimate flow are converted to nonlinear ordinary differential equations(ODEs)using appropriate similarity transformation.The ODEs are dealt with numerically by means of MATLAB’s inbuilt routine function bvp4c.Velocity,temperature,and concentration profiles are explained pictorially whereas Sherwood number,local skin friction coefficient,and Nusselt number values are represented through bar charts.Thermal radiation and activation parameters shows direct impact on flow field.Furthermore,hybrid nanofluid admits a higher magnitude of velocity and temperature than nanofluid,but the concentration profile exhibits the opposite trend.The notable findings of the present investigation have significant applications in heat combustion and cooling chambers,space technology,the ceramics industry,paint and conductive coatings,bio-sensors,and many more.

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

Stability Analysis of Predator-Prey System with Consuming Resource and Disease in Predator Species

The present study is concerned with formulating a predator-prey eco-epidemiological mathematical model assuming that an infection exists in the predator species.The two classes of predator species(susceptible and infected)compete for the same sources available in the environment with the predation option.It is assumed that the disease does not spread vertically.The proposed model is analyzed for the stability of the coexistence of the predators and prey.The fixed points are carried out,and the coexisting fixed point is studied in detail by constructing the Lyapunov function.The movement of species in search of food or protection in their habitat has a significant influence,examined through diffusion.The ecological influences of self-diffusion on the population density of both species are studied.It is theoretically proved that all the under consideration species can coexist in the same environment.The coexistence fixed point is discussed for both diffusive and non-diffusive cases.Moreover,a numerical scheme is constructed for solving time-dependent partial differential equations.The stability of the scheme is given,and it is applied for solving presently modified eco-epidemiological mathematical model with and without diffusion.The comparison of the constructed scheme with two exiting schemes,Backward in Time and Central in Space(BTCS)and Crank Nicolson,is also given in the form of plots.Finally,we run a computer simulation to determine the effectiveness of the proposed numerical scheme.For readers’convenience,a computational code for the proposed discrete model scheme may be made available upon request.

Construction and Optimization of TRNG Based Substitution Boxes for Block Encryption Algorithms

Internet of Things is an ecosystem of interconnected devices that are accessible through the internet.The recent research focuses on adding more smartness and intelligence to these edge devices.This makes them susceptible to various kinds of security threats.These edge devices rely on cryptographic techniques to encrypt the pre-processed data collected from the sensors deployed in the field.In this regard,block cipher has been one of the most reliable options through which data security is accomplished.The strength of block encryption algorithms against different attacks is dependent on its nonlinear primitive which is called Substitution Boxes.For the design of S-boxes mainly algebraic and chaos-based techniques are used but researchers also found various weaknesses in these techniques.On the other side,literature endorse the true random numbers for information security due to the reason that,true random numbers are purely non-deterministic.In this paper firstly a natural dynamical phenomenon is utilized for the generation of true random numbers based S-boxes.Secondly,a systematic literature review was conducted to know which metaheuristic optimization technique is highly adopted in the current decade for the optimization of S-boxes.Based on the outcome of Systematic Literature Review(SLR),genetic algorithm is chosen for the optimization of s-boxes.The results of our method validate that the proposed dynamic S-boxes are effective for the block ciphers.Moreover,our results showed that the proposed substitution boxes achieve better cryptographic strength as compared with state-of-the-art techniques.

Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

In this work,we present a model that uses the fractional order Caputo derivative for the novel Coronavirus disease 2019(COVID-19)with different hospitalization strategies for severe and mild cases and incorporate an awareness program.We generalize the SEIR model of the spread of COVID-19 with a private focus on the transmissibility of people who are aware of the disease and follow preventative health measures and people who are ignorant of the disease and do not follow preventive health measures.Moreover,individuals with severe,mild symptoms and asymptomatically infected are also considered.The basic reproduction number(R0)and local stability of the disease-free equilibrium(DFE)in terms of R0 are investigated.Also,the uniqueness and existence of the solution are studied.Numerical simulations are performed by using some real values of parameters.Furthermore,the immunization of a sample of aware susceptible individuals in the proposed model to forecast the effect of the vaccination is also considered.Also,an investigation of the effect of public awareness on transmission dynamics is one of our aim in this work.Finally,a prediction about the evolution of COVID-19 in 1000 days is given.For the qualitative theory of the existence of a solution,we use some tools of nonlinear analysis,including Lipschitz criteria.Also,for the numerical interpretation,we use the Adams-Moulton-Bashforth procedure.All the numerical results are presented graphically.

Theory and Semi-Analytical Study of Micropolar Fluid Dynamics through a Porous Channel

In this work,We are looking at the characteristics of micropolar flow in a porous channel that’s being driven by suction or injection.The working of the fluid is described in the flowmodel.We can reduce the governing nonlinear partial differential equations(PDEs)to a model of coupled systems of nonlinear ordinary differential equations using similarity variables(ODEs).In order to obtain the results of a coupled system of nonlinear ODEs,we discuss a method which is known as the differential transform method(DTM).The concern transform is an excellent mathematical tool to obtain the analytical series solution to the nonlinear ODEs.To observe beast agreement between analytical method and numerical method,we compare our result with the Rung-Kutta method of order four(RK4).We also provide simulation plots to the obtained result by using Mathematica.Onthese plots,we discuss the effect of different parameters which arise during the calculation of the flow model equations.

Fixed Points and Asymptotic Properties of Neutral Stochastic Delay Differential Equations

This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.

Numerical computations of magnetohydrodynamic mixed convective flow of Casson nanofluid in an open-ended cavity formed by earthquake-induced faults

The numerical computations for the magnetohydrodynamic(MHD) mixed convective flow of a non-Newtonian Casson nanofluid(Cu/H2O) within an open-ended cavity formed by earthquake-induced faults are analyzed, aiming to investigate the fluid dynamics and convection processes of geothermal systems. Such cavities, typically found in energy reservoirs, are primarily caused by tensional fault zones formed due to the accumulated energy from the disintegration of radioactive materials. These cavities play a crucial role in energy transmission, particularly in the form of heat. The focus of this paper is on the laminar, steady, and incompressible fluid flow. An inclined magnetic field is applied with an angle of inclination z = 30°. Additionally, a heated material with two vertical corrugated walls is placed at the center of the cavity. The governing nonlinear partial differential equations(PDEs) are transformed into the equations with a nondimensional form. The Galerkin finite element method(FEM) is implemented to solve the dimensionless equations. The impacts of key variables, including the Reynolds number Re, the volume fraction(0.01≤ φ_(p)≤0.05), the Hartmann number Ha, and the Casson parameter(0.5≤γ≤1.0), on the velocity and temperature distributions are studied. The analysis of the fluid flow and the heat transfer rate is conducted. The results indicate that the velocity increases as the volume fraction and the Reynolds number increase.Similarly, the heat transfer rate rises with the Reynolds number and the volume fraction,while decreases with the higher Hartmann number. The Nusselt number increases with the volume fraction and the Reynolds number but decreases with the Hartmann number.

A Dynamical Study of Modeling the Transmission of Typhoid Fever throughDelayed Strategies

This study analyzes the transmission of typhoid fever caused by Salmonella typhi using a mathematical model thathighlights the significance of delay in its effectiveness.Time delays can affect the nature of patterns and slow downthe emergence of patterns in infected population density.The analyzed model is expanded with the equilibriumanalysis,reproduction number,and stability analysis.This study aims to establish and explore the non-standardfinite difference(NSFD)scheme for the typhoid fever virus transmission model with a time delay.In addition,the forward Euler method and Runge-Kutta method of order 4(RK-4)are also applied in the present research.Some significant properties,such as convergence,positivity,boundedness,and consistency,are explored,and theproposed scheme preserves all the mentioned properties.The theoretical validation is conducted on how NSFDoutperforms other methods in emulating key aspects of the continuous model,such as positive solution,stability,and equilibrium about delay.Hence,the above analysis also shows some of the limitations of the conventional finitedifference methods,such as forward Euler and RK-4 in simulating such critical behaviors.This becomes moreapparent when using larger steps.This indicated that NSFD is beneficial in identifying the essential characteristicsof the continuous model with higher accuracy than the traditional approaches.

Computational Modeling of Reaction-Diffusion COVID-19 Model Having Isolated Compartment

Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are calculated.

Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative

This research aims to understand the fractional order dynamics of the deadly Nipah virus(NiV)disease.We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical system.We establish some qualitative results about the existence and uniqueness of the solution to the proposed problem.By utilizing the Newtonian polynomials interpolation technique,we recall a powerful algorithm to interpret the numerical findings for the aforesaid model.Here,we remark that the said viral infection is caused by an RNA type virus which can transmit from animals and also from an infected person to person.Fruits bats which are also known as flying foxes are one of the sources of transmission of NiV disease.Here in this work,we investigate its transmission mechanism through some new concepts of fractional calculus for further analysis and prediction.We present the approximate results for different compartments using different fractional orders.By using the piecewise derivative concept,we detect the crossover ormulti-steps behavior in the transmission dynamics of the mentioned disease.Therefore,the considered form of the derivative is used to deal with problems exhibiting crossover behaviors.

Electrochemical determination of an anti-hyperlipidimic drug pitavastatin at electrochemical sensor based on electrochemically pre-treated polymer film modified GCE

An electrochemically pretreated silver macroporous(Ag MP) multiwalled carbon nanotube modified glassy carbon electrode(PAN-Ag MP-MWCNT-GCE) was fabricated for the selective determination of an antihyperlipidimic drug, pitavastatin(PST). The fabricated electrochemical sensor was characterized by cyclic voltammetry(CV) and electrochemical impedance spectroscopy(EIS). The fabricated electrode was employed in quantifying and determining PST through differential pulse adsorptive stripping voltammetry(DPAdSV) and CV. The electrode fabrication proceeded with remarkable sensitivity to the determination of PST. The effect of various optimized parameters such as pH, scan rate(ν), accumulation time(t_(acc)), accumulation potential(U_(acc))and loading volumes of Ag MP-MWCNT suspension were investigated to evaluate the performance of synthesized electrochemical sensor and to propose a simple, accurate, rapid and economical procedure for the quantification of PST in pharmaceutical formulations and biological fluids. A linear response of PST concentration in the range 2.0×10^(-7)–1.6×10^(-6)M with low detection(LOD) and quantification(LOQ) limits of 9.66 ± 0.04 nM and 32.25 ± 0.07 nM, respectively, were obtained under these optimized conditions.

A Theoretical Investigation of the SARS-CoV-2Model via Fractional Order Epidemiological Model

We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in 2019.We develop a mathematical model based on the novel corona virus’s characteristics and then use fractional calculus to fractionalize it.Various fractional order epidemicmodels have been formulated and analyzed using a number of iterative and numerical approacheswhile the complications arise due to singular kernel.We use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular kernel.Moreover,to analyze the existence and uniqueness,we will use the well-known fixed point theory.We also prove that the considered model has positive and bounded solutions.We also draw some numerical simulations to verify the theoretical work via graphical representations.We believe that the proposed epidemic model will be helpful for health officials to take some positive steps to control contagious diseases.

Numerical Study for Magnetohydrodynamic(MHD)Unsteady Maxwell Nanofluid Flow Impinging on Heated Stretching Sheet

The numerous applications of Maxwell Nanofluid Stagnation Point Flow,such as those in production industries,the processing of polymers,compression,power generation,lubrication systems,food manufacturing and air conditioning,among other applications,require further research into the effects of various parameters on flow phenomena.In this paper,a study has been carried out for the heat andmass transfer of Maxwell nanofluid flow over the heated stretching sheet.A mathematical model with constitutive expressions is constructed in partial differential equations(PDEs)through obligatory basic conservation laws.A series of transformations are then used to take the system into an ordinary differential equation(ODE).The boundary conditions(BCs)are also treated similarly for transforming into first-order ordinary differential equations(ODEs).Then these ODEs are computed by using the Shooting Method.The effect of factors on the skin friction coefficient,the local Nusselt number,and the local Sherwood number are explored,and the results are displayed graphically.The obtained results demonstrate that by increasing the values of the Maxwell and slip velocity parameters,velocity deescalates.For investigators tasked with addressing unresolved difficulties in the realm of enclosures used in industry and engineering,we thought this work would serve as a guide.

On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.

A Thermal Shock-Chemical Reactive Problem in Flow of Viscoelastic Fluid with Thermal Relaxation

Effects of thermal and species diffusion with one relaxation time on the boundary layer flow of a viscoelastic fluid bounded by a vertical surface in the presence of transverse magnetic field have been studied. The state space approach developed by Ezzat [1] is adopted for the solution of one-dimensional problem for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a thermal shock-chemical reactive problem. The inversion of the Laplace transforms is carried out using a numerical approach. The numerical results of dimensionless temperature, concentration, velocity, and induced magnetic and electric fields distributions are given and illustrated graphically for the problem.

Numerical Solutions of Fractional Variable Order Differential Equations via Using Shifted Legendre Polynomials

In this manuscript,an algorithm for the computation of numerical solutions to some variable order fractional differential equations(FDEs)subject to the boundary and initial conditions is developed.We use shifted Legendre polynomials for the required numerical algorithm to develop some operational matrices.Further,operational matrices are constructed using variable order differentiation and integration.We are finding the operationalmatrices of variable order differentiation and integration by omitting the discretization of data.With the help of aforesaid matrices,considered FDEs are converted to algebraic equations of Sylvester type.Finally,the algebraic equations we get are solved with the help of mathematical software like Matlab or Mathematica to compute numerical solutions.Some examples are given to check the proposed method’s accuracy and graphical representations.Exact and numerical solutions are also compared in the paper for some examples.The efficiency of the method can be enhanced further by increasing the scale level.