A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential EquationModel for HIV/AIDS with Treatment Compartment

In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.

Country-based modelling of COVID-19 case fatality rate:A multiple regression analysis

BACKGROUND The spread of the severe acute respiratory syndrome coronavirus 2 outbreak worldwide has caused concern regarding the mortality rate caused by the infection.The determinants of mortality on a global scale cannot be fully understood due to lack of information.AIM To identify key factors that may explain the variability in case lethality across countries.METHODS We identified 21 Potential risk factors for coronavirus disease 2019(COVID-19)case fatality rate for all the countries with available data.We examined univariate relationships of each variable with case fatality rate(CFR),and all independent variables to identify candidate variables for our final multiple model.Multiple regression analysis technique was used to assess the strength of relationship.RESULTS The mean of COVID-19 mortality was 1.52±1.72%.There was a statistically significant inverse correlation between health expenditure,and number of computed tomography scanners per 1 million with CFR,and significant direct correlation was found between literacy,and air pollution with CFR.This final model can predict approximately 97%of the changes in CFR.CONCLUSION The current study recommends some new predictors explaining affect mortality rate.Thus,it could help decision-makers develop health policies to fight COVID-19.

Measurement Research Based on Bayesian Structural Equation Cognitive Model

The Bayesian structural equation model integrates the principles of Bayesian statistics, providing a more flexible and comprehensive modeling framework. In exploring complex relationships between variables, handling uncertainty, and dealing with missing data, the Bayesian structural equation model demonstrates unique advantages. Therefore, Bayesian methods are used in this paper to establish a structural equation model of innovative talent cognition, with the measurement of college students’ cognition of innovative talent being studied. An in-depth analysis is conducted on the effects of innovative self-efficacy, social resources, innovative personality traits, and school education, aiming to explore the factors influencing college students’ innovative talent. The results indicate that innovative self-efficacy plays a key role in perception, social resources are significantly positively correlated with the perception of innovative talents, innovative personality tendencies and school education are positively correlated with the perception of innovative talents, but the impact is not significant.

The Time-Consistent Optimal Reinsurance Strategy of Insurance Group under the CEV Model

The article introduces proportional reinsurance contracts under the mean-variance criterion,studying the time-consistence investment portfolio problem considering the interests of both insurance companies and reinsurance companies.The insurance claims process follows a jump-diffusion model,assuming that the risk asset prices of insurance companies and reinsurance companies follow CEV models different from each other.In the framework of game theory,the time-consistent equilibrium reinsurance strategy is obtained by solving the extended HJB equation analytically.Finally,numerical examples are used to illustrate the impact of model parameters on equilibrium strategies and provide economic explanations.The results indicate that the decision weights of insurance companies and reinsurance companies do have a significant impact on both the reinsurance ratio and the equilibrium reinsurance strategy.

Evaluation of the Impact of Refined Quality Control Management Model on the Qualified Rate of Disinfection and Sterilization of Surgical Instruments in the Sterilization Supply Center

Objective:To evaluate the application value of a refined quality control management model for a sterilization supply center.Methods:A retrospective analysis was conducted on the work situation of the sterilization supply center from January 2021 to January 2023.The work situation before January 31,2022,was classified as the control group;a routine quality control management model was implemented,and the work situation after January 31,2022,was classified as the observation group.The quality of medical device management and department satisfaction between the two groups were compared.Results:The timely recovery and supply rate,classification and cleaning pass rate,disinfection pass rate,packaging pass rate,sterilization pass rate,and department satisfaction score in the observation group were all higher than those of the control group(P<0.05).Conclusion:Implementing a refined quality control management model in the sterilization supply center can improve the quality management level of medical devices and department satisfaction and is worthy of promotion.

Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

Federated Learning Model for Auto Insurance Rate Setting Based on Tweedie Distribution

In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.

Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.

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.

INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM

In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.

Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry.To study the mechanical behavior of a typical ductile cast iron(GJS-450)with nodular graphite,uni-axial quasi-static and dynamic tensile tests at strain rates of 10^(-4),1,10,100,and 250 s^(-1)were carried out.In order to investigate the influence of stress state on the deformation and fracture parameters,specimens with various geometries were used in the experiments.Stress strain curves and fracture strains of the GJS-450 alloy in the strain rate range of 10^(-4)to 250 s^(-1)were obtained.A strain rate-dependent plastic flow model was proposed to describe the mechanical behavior in the corresponding strain-rate range.The available damage model was extended to take the strain rate into account and calibrated based on the analysis of local fracture strains.Simulations with the proposed plastic flow model and the damage model were conducted to observe the deformation and fracture process.The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys.The predictions with the proposed plastic flow and damage models at various strain rates agree well with the experimental results,which illustrates that the rate-dependent plastic flow and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.The proposed plastic flow and damage models can be used to describe the deformation and fracture analysis of materials with similar properties.

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

Accurate simulations of pure-viscoacoustic wave propagation in tilted transversely isotropic media

Forward modeling of seismic wave propagation is crucial for the realization of reverse time migration(RTM) and full waveform inversion(FWI) in attenuating transversely isotropic media. To describe the attenuation and anisotropy properties of subsurface media, the pure-viscoacoustic anisotropic wave equations are established for wavefield simulations, because they can provide clear and stable wavefields. However, due to the use of several approximations in deriving the wave equation and the introduction of a fractional Laplacian approximation in solving the derived equation, the wavefields simulated by the previous pure-viscoacoustic tilted transversely isotropic(TTI) wave equations has low accuracy. To accurately simulate wavefields in media with velocity anisotropy and attenuation anisotropy, we first derive a new pure-viscoacoustic TTI wave equation from the exact complex-valued dispersion formula in viscoelastic vertical transversely isotropic(VTI) media. Then, we present the hybrid finite-difference and low-rank decomposition(HFDLRD) method to accurately solve our proposed pure-viscoacoustic TTI wave equation. Theoretical analysis and numerical examples suggest that our pure-viscoacoustic TTI wave equation has higher accuracy than previous pure-viscoacoustic TTI wave equations in describing q P-wave kinematic and attenuation characteristics. Additionally, the numerical experiment in a simple two-layer model shows that the HFDLRD technique outperforms the hybrid finite-difference and pseudo-spectral(HFDPS) method in terms of accuracy of wavefield modeling.

Comparisons of Wave Force Model Effects on the Structural Responses and Fatigue Loads of a Semi-Submersible Floating Wind Turbine

The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.

Numerical three-dimensional modeling of earthen dam piping failure

A physically-based numerical three-dimensional earthen dam piping failure model is developed for homogeneous and zoned soil dams.This model is an erosion model,coupled with force/moment equilibrium analyses.Orifice flow and two-dimensional(2D)shallow water equations(SWE)are solved to simulate dam break flows at different breaching stages.Erosion rates of different soils with different construction compaction efforts are calculated using corresponding erosion formulae.The dam's real shape,soil properties,and surrounding area are programmed.Large outer 2D-SWE grids are used to control upstream and downstream hydraulic conditions and control the boundary conditions of orifice flow,and inner 2D-SWE flow is used to scour soil and perform force/moment equilibrium analyses.This model is validated using the European Commission IMPACT(Investigation of Extreme Flood Processes and Uncertainty)Test#5 in Norway,Teton Dam failure in Idaho,USA,and Quail Creek Dike failure in Utah,USA.All calculated peak outflows are within 10%errors of observed values.Simulation results show that,for a V-shaped dam like Teton Dam,a piping breach location at the abutment tends to result in a smaller peak breach outflow than the piping breach location at the dam's center;and if Teton Dam had broken from its center for internal erosion,a peak outflow of 117851 m'/s,which is 81%larger than the peak outflow of 65120 m3/s released from its right abutment,would have been released from Teton Dam.A lower piping inlet elevation tends to cause a faster/earlier piping breach than a higher piping inlet elevation.

RETRACTED: Nuclear Structure Study of Odd-Odd Yttrium Nuclei within Interacting-Boson Fermi-Fermion Model (IBFFM)

Short Retraction NoticeThe paper does not meet the standards of "Journal of Applied Mathematics and Physics". This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.Editor guiding this retraction: Prof. Wen-Xiu Ma (EiC of JAMP)The full retraction notice in PDF is preceding the original paper, which is marked "RETRACTED".

Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

A new Ignition-Growth reaction rate model for shock initiation

Accurately predicting reactive flow is a challenge when characterizing an explosive under external shock stimuli as the shock initiation time is on the order of a microsecond.The present study constructs a new Ignition-Growth reaction rate model,which can describe the shock initiation processes of explosives with different initial densities,particle sizes and loading pressures by only one set of model parameters.Compared with the Lee-Tarver reaction rate model,the new Ignition-Growth reaction rate model describes better the shock initiation process of explosives and requires fewer model parameters.Moreover,the shock initiation of a 2,4-Dinitroanisole(DNAN)-based melt-cast explosive RDA-2(DNAN/HMX(octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine)/aluminum)are investigated both experimentally and numerically.A series of shock initiation experiments is performed with manganin piezoresistive pressure gauges and corresponding numerical simulations are carried out with the new Ignition-Growth reaction rate model.The RDA-2 explosive is found to have higher critical initiation pressure and lower shock sensitivity than traditional explosives(such as the Comp.B explosive).The calibrated reaction rate model parameters of RDA-2 could provide numerical basis for its further application.

Modeling the Failure Rate of a Standby Multi-Component System and Improving Reliability

Evaluating the reliability of a system requires knowledge of the failure modes to which it is subjected. Complex topology systems generally require a high level of availability, which is a function of the arrangement of elements (components) in the system. To avoid serious failures for such complex systems, recourse can be had to the redundancy techniques available in the literature. These techniques help to improve system reliability, without affecting the reliability of system components. This paper is interested in the proposal of a model for evaluating the failure rate of a standby multi-components system and in improving the reliability of mechanical systems, arranged in a topology (series, parallel, or mixed).

Empirical Research on the Relationship between Education Poverty Alleviation and Rural Revitalization—Spatial Panel Simultaneous Equation Model Based on Provincial Panel Data

On the basis of using entropy weight method to measure China’s education poverty alleviation and rural revitalization evaluation indicators, using the panel data of 30 provinces in China (excluding Xizang, Hong Kong, Macao and Taiwan) from 2012 to 2021, a spatial panel simultaneous equation model is constructed based on adjacency matrix, geographical distance matrix and economic geographical distance matrix deeply study the interaction mechanism and spatial spillover effects between education poverty alleviation and rural revitalization through the generalized spatial three-stage least squares method (GS3SLS). The results indicate that there is a significant spatial spillover effect and a positive spatial correlation between education poverty alleviation and rural revitalization, and there is a significant interactive effect between the two variables, while promoting each other positively. Therefore, the government should clarify the deep relationship between education poverty alleviation and rural revitalization based on the current background, and better consolidate and expand the effective connection between the achievements of education poverty alleviation and rural revitalization.