The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal ...The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal counterparts,one gains insights into the system's response under new mathematical frameworks.This paper presents a novel method for converting standard continuous differential equations into their fractal equivalents.This conversion occurs after the nonlinear system is transformed into its linear equivalent.Numerical analyses show that there are several resonance sites in the fractal system,which differ from the one resonance point found in the continuous system.One important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse pattern.Interestingly,a decrease in the fractal order in resonance settings shows a stabilizing impact,highlighting the dynamics'complexity inside fractal systems.This endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.展开更多
BACKGROUND Diabetic foot(DF)is a serious complication of type 2 diabetes.This study aimed to investigate the factors associated with DF occurrence and the role of delayed medical care in a cohort of patients with type...BACKGROUND Diabetic foot(DF)is a serious complication of type 2 diabetes.This study aimed to investigate the factors associated with DF occurrence and the role of delayed medical care in a cohort of patients with type 2 diabetes.AIM To reveal the impact of delayed medical treatment on the development of DF in patients with type 2 diabetes and to establish a predictive model for DF.METHODS In this retrospective cohort study,292 patients with type 2 diabetes who underwent examination at our hospital from January 2023 to December 2023 were selected and divided into the DF group(n=82,DF)and nondiabetic foot group(n=210,NDF).Differential and correlation analyses of demographic indicators,laboratory parameters,and delayed medical treatment were conducted for the two groups.Logistic regression was applied to determine influencing factors.Receiver operating characteristic(ROC)analysis was performed,and indicators with good predictive value were selected to establish a combined predictive model.RESULTS The DF group had significantly higher body mass index(BMI)(P<0.001),disease duration(P=0.012),plasma glucose levels(P<0.001),and HbA1c(P<0.001)than the NDF group.The NDF group had significantly higher Acute Thrombosis and Myocardial Infarction Health Service System(ATMHSS)scores(P<0.001)and a significantly lower delayed medical treatment rate(72.38%vs 13.41%,P<0.001).BMI,duration of diabetes,plasma glucose levels,HbA1c,diabetic peripheral neuropathy,and nephropathy were all positively correlated with DF occurrence.ATMHSS scores were negatively correlated with delayed time to seek medical treatment.The logistic regression model revealed that BMI,duration of diabetes,plasma glucose levels,HbA1c,presence of diabetic peripheral neuropathy and nephropathy,ATMHSS scores,and delayed time to seek medical treatment were influencing factors for DF.ROC analysis indicated that plasma glucose levels,HbA1c,and delayed medical treatment had good predictive value with an area under the curve of 0.933 for the combined predictive model.CONCLUSION Delayed medical treatment significantly affects the probability of DF occurrence in patients with diabetes.Plasma glucose levels,HbA1c levels,and the combined predictive model of delayed medical treatment demonstrate good predictive value.展开更多
In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave so...In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.展开更多
In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and co...In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and construct suitable functions to obtain sufficient conditions for disease extinction.Secondly,in order to effectively control the spread of the disease,appropriate control strategies are formulated by using optimal control theory.Finally,the results are verified by numerical simulation.展开更多
Zenith wet delay(ZWD)is a key parameter for the precise positioning of global navigation satellite systems(GNSS)and occupies a central role in meteorological research.Currently,most models only consider the periodic v...Zenith wet delay(ZWD)is a key parameter for the precise positioning of global navigation satellite systems(GNSS)and occupies a central role in meteorological research.Currently,most models only consider the periodic variability of the ZWD,neglecting the effect of nonlinear factors on the ZWD estimation.This oversight results in a limited capability to reflect the rapid fluctuations of the ZWD.To more accurately capture and predict complicated variations in ZWD,this paper developed the CRZWD model by a combination of the GPT3 model and random forests(RF)algorithm using 5-year atmospheric profiles from 70 radiosonde(RS)stations across China.Taking the external 25 test stations data as reference,the root mean square(RMS)of the CRZWD model is 29.95 mm.Compared with the GPT3 model and another model using backpropagation neural network(BPNN),the accuracy has improved by 24.7%and 15.9%,respectively.Notably,over 56%of the test stations exhibit an improvement of more than 20%in contrast to GPT3-ZWD.Further temporal and spatial characteristic analyses also demonstrate the significant accuracy and stability advantages of the CRZWD model,indicating the potential prospects for GNSS-based applications.展开更多
In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6...In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.展开更多
The repair of the periodontal membrane is essential for the successful management of periodontal disease and dental trauma.Emdogain®(EMD)is widely used in periodontal therapy due to its ability to promote repair....The repair of the periodontal membrane is essential for the successful management of periodontal disease and dental trauma.Emdogain®(EMD)is widely used in periodontal therapy due to its ability to promote repair.Despite substantial research,the cellular and molecular mechanisms underlying EMD’s effects,particularly at the single-cell resolution,remain incompletely understood.This study established a delayed tooth replantation model in rats to investigate these aspects.Tooth loss rate and degree of loosening were evaluated at 4 and 8 weeks.Micro-CT,HE staining,TRAP staining,and immunofluorescence staining were evaluated to assess EMD’s efficacy.Single-cell sequencing analyses generated single-cell maps that explored enrichment pathways,cell communication,and potential repair mechanisms.Findings indicated that EMD could reduce the rate of tooth loss,promote periodontal membrane repair,and reduce root and bone resorption.Single-cell analysis revealed that EMD promotes the importance of Vtn+fibroblasts,enhancing matrix and tissue regeneration functions.Additionally,EMD stimulated osteogenic pathways,reduced osteoclastic activity,and promoted angiogenesis-related pathways,particularly bone-related H-type vessel expression in endothelial cells.Gene modules associated with angiogenesis,osteogenesis,and odontoblast differentiation were identified,suggesting EMD might facilitate osteogenesis and odontoblast differentiation by upregulating endothelium-related genes.Immune cell analysis indicated that EMD did not elicit a significant immune response.Cell communication analysis suggested that EMD fostered pro-regenerative networks driven by interactions between mesenchymal stem cells,fibroblasts,and endothelial cells.In conclusion,EMD proves to be an effective root surface therapy agent that supports the restoration of delayed replantation teeth.展开更多
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 glob...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.展开更多
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 a...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.展开更多
Background:Paraplegia after spinal cord ischemia is a devastating condition in the clinic.Here,we develop an awake rabbit model of spinal cord ischemia with delayed paraplegia and explore the influence of ambient temp...Background:Paraplegia after spinal cord ischemia is a devastating condition in the clinic.Here,we develop an awake rabbit model of spinal cord ischemia with delayed paraplegia and explore the influence of ambient temperature on the outcomes after injury.Methods:A total of 47 male rabbits were involved in the present study.Transient spinal cord ischemia was induced by occluding the infrarenal abdominal aorta of awake rabbits at different ambient temperatures.To find the optimal conditions for developing delayed paraplegia,hindlimb motor function after ischemia was evaluated between experiments.Results:The onset and magnitude of ischemic injury varied with the ambient temperature maintained during the peri-i schemia period.More serious spinal cord injury occurred when ischemia was induced at higher temperatures.At 18°C,25-minute ischemia resulted in 74%of rabbits developing delayed paraplegia.At a temperature of 28°C or higher,most of the animals developed acute paraplegia immediately.While at 13°C,rabbits usually regained normal motor function without paraplegia.Conclusion:This awake rabbit model is highly reproducible and will be helpful in future studies of delayed paraplegia after spinal cord ischemia.The ambient temperature must be considered while using this model during investigation of therapeutic interventions.展开更多
Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challeng...Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.展开更多
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 wi...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 R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.展开更多
Delayed coking is an important process consumption and light oil yield are important factors used to convert heavy oils to light products. Energy for evaluating the delayed coking process. This paper analyzes the ener...Delayed coking is an important process consumption and light oil yield are important factors used to convert heavy oils to light products. Energy for evaluating the delayed coking process. This paper analyzes the energy consumption and product yields of delayed coking units in China. The average energy consumption shows a decreasing trend in recent years. The energy consumption of different refineries varies greatly, with the average value of the highest energy consumption approximately twice that of the lowest energy consumption. The factors affecting both energy consumption and product yields were analyzed, and correlation models of energy consumption and product yields were established using a quadratic polynomial. The model coefficients were calculated through least square regression of collected industrial data of delayed coking units. Both models showed good calculation accuracy. The average absolute error of the energy consumption model was approximately 85 MJ/t, and that of the product yield model ranged from 1 wt% to 2.3 wt%. The model prediction showed that a large annual processing capacity and high load rate will result in a reduction in energy consumption.展开更多
Mathematical delay modelling has a significant role in the different disciplines such as behavioural,social,physical,biological engineering,and bio-mathematical sciences.The present work describes mathematical formula...Mathematical delay modelling has a significant role in the different disciplines such as behavioural,social,physical,biological engineering,and bio-mathematical sciences.The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus(COVID-19).Due to the unavailability of vaccines for the coronavirus worldwide,delay factors such as social distance,quarantine,travel restrictions,extended holidays,hospitalization,and isolation have contributed to controlling the coronavirus epidemic.We have analysed the reproduction number and its sensitivity to parameters.If,R_(covid)>1then this situation will help to eradicate the disease and if,R_(covid)>1 the virus will spread rapidly in the human beings.Well-known theorems such as Routh Hurwitz criteria and Lasalle invariance principle have presented for stability.The local and global stabilizes for both equilibria of the model have also been presented.Also,we have analysed the effect of delay reason on the reproduction number.In the last,some very useful numerical consequences have presented in support of hypothetical analysis.展开更多
Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue lengt...Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue length is investigated in detail. The main advantage of the new model is that its stability domain is larger even without an extra controller. By linear stability analysis and numerical simulation, tbe effectiveness and feasibility of the novel model in internet congestion control are verified.展开更多
The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identific...The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix(HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.展开更多
In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model h...In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.展开更多
The precise correction of atmospheric zenith tropospheric delay(ZTD)is significant for the Global Navigation Satellite System(GNSS)performance regarding positioning accuracy and convergence time.In the past decades,ma...The precise correction of atmospheric zenith tropospheric delay(ZTD)is significant for the Global Navigation Satellite System(GNSS)performance regarding positioning accuracy and convergence time.In the past decades,many empirical ZTD models based on whether the gridded or scattered ZTD products have been proposed and widely used in the GNSS positioning applications.But there is no comprehensive evaluation of these models for the whole China region,which features complicated topography and climate.In this study,we completely assess the typical empirical models,the IGGtropSH model(gridded,non-meteorology),the SHAtropE model(scattered,non-meteorology),and the GPT3 model(gridded,meteorology)using the Crustal Movement Observation Network of China(CMONOC)network.In general,the results show that the three models share consistent performance with RMSE/bias of 37.45/1.63,37.13/2.20,and 38.27/1.34 mm for the GPT3,SHAtropE and IGGtropSH model,respectively.However,the models had a distinct performance regarding geographical distribution,elevation,seasonal variations,and daily variation.In the southeastern region of China,RMSE values are around 50 mm,which are much higher than that in the western region,approximately 20 mm.The SHAtropE model exhibits better performance for areas with large variations in elevation.The GPT3 model and the IGGtropSH model are more stable across different months,and the SHAtropE model based on the GNSS data exhibits superior performance across various UTC epochs.展开更多
The performance of the model algorithm control method is partially based on the accuracy of the system＇s model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. ...The performance of the model algorithm control method is partially based on the accuracy of the system＇s model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. Neural networks have the ability to ＂learn＂the characteristics of a system through nonlinear mapping to represent nonlinear functions as well as their inverse functions. This paper presents a model algorithm control method using neural networks for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one produces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to illustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.展开更多
Through the study,the nonlinear delayed modelling has vital significance in the different field of allied sciences like computational biology,computational chemistry,computational physics,computational economics and m...Through the study,the nonlinear delayed modelling has vital significance in the different field of allied sciences like computational biology,computational chemistry,computational physics,computational economics and many more.Polio is a contagious viral illness that in its most severe form causes nerve injury leading to paralysis,difficulty breathing and sometimes death.In recent years,developing regions like Asia,Africa and sub-continents facing a dreadful situation of poliovirus.That is the reason we focus on the treatment of the polio epidemic model with different delay strategies in this article.Polio delayed epidemic model is categorized into four compartments like susceptible,exposed,infective and vaccinated classes.The equilibria,positivity,boundedness,and reproduction number are investigated.Also,the sensitivity of the parameters is analyzed.Well,known results like the Routh Hurwitz criterion and Lyapunov function stabilities are investigated for polio delayed epidemic model in the sense of local and global respectively.Furthermore,the computer simulations are presented with different traditions in the support of the analytical analysis of the polio delayed epidemic model.展开更多
文摘The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal counterparts,one gains insights into the system's response under new mathematical frameworks.This paper presents a novel method for converting standard continuous differential equations into their fractal equivalents.This conversion occurs after the nonlinear system is transformed into its linear equivalent.Numerical analyses show that there are several resonance sites in the fractal system,which differ from the one resonance point found in the continuous system.One important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse pattern.Interestingly,a decrease in the fractal order in resonance settings shows a stabilizing impact,highlighting the dynamics'complexity inside fractal systems.This endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.
文摘BACKGROUND Diabetic foot(DF)is a serious complication of type 2 diabetes.This study aimed to investigate the factors associated with DF occurrence and the role of delayed medical care in a cohort of patients with type 2 diabetes.AIM To reveal the impact of delayed medical treatment on the development of DF in patients with type 2 diabetes and to establish a predictive model for DF.METHODS In this retrospective cohort study,292 patients with type 2 diabetes who underwent examination at our hospital from January 2023 to December 2023 were selected and divided into the DF group(n=82,DF)and nondiabetic foot group(n=210,NDF).Differential and correlation analyses of demographic indicators,laboratory parameters,and delayed medical treatment were conducted for the two groups.Logistic regression was applied to determine influencing factors.Receiver operating characteristic(ROC)analysis was performed,and indicators with good predictive value were selected to establish a combined predictive model.RESULTS The DF group had significantly higher body mass index(BMI)(P<0.001),disease duration(P=0.012),plasma glucose levels(P<0.001),and HbA1c(P<0.001)than the NDF group.The NDF group had significantly higher Acute Thrombosis and Myocardial Infarction Health Service System(ATMHSS)scores(P<0.001)and a significantly lower delayed medical treatment rate(72.38%vs 13.41%,P<0.001).BMI,duration of diabetes,plasma glucose levels,HbA1c,diabetic peripheral neuropathy,and nephropathy were all positively correlated with DF occurrence.ATMHSS scores were negatively correlated with delayed time to seek medical treatment.The logistic regression model revealed that BMI,duration of diabetes,plasma glucose levels,HbA1c,presence of diabetic peripheral neuropathy and nephropathy,ATMHSS scores,and delayed time to seek medical treatment were influencing factors for DF.ROC analysis indicated that plasma glucose levels,HbA1c,and delayed medical treatment had good predictive value with an area under the curve of 0.933 for the combined predictive model.CONCLUSION Delayed medical treatment significantly affects the probability of DF occurrence in patients with diabetes.Plasma glucose levels,HbA1c levels,and the combined predictive model of delayed medical treatment demonstrate good predictive value.
基金Supported by the National Natural Science Foundation of China(12261050)Science and Technology Project of Department of Education of Jiangxi Province(GJJ2201612 and GJJ211027)Natural Science Foundation of Jiangxi Province of China(20212BAB202021)。
文摘In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.
基金supported by the Fundamental Research Funds for the Central Universities(No.3122025090)。
文摘In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and construct suitable functions to obtain sufficient conditions for disease extinction.Secondly,in order to effectively control the spread of the disease,appropriate control strategies are formulated by using optimal control theory.Finally,the results are verified by numerical simulation.
基金supported by the National Natural Science Foundation of China[42030109,42074012]the Scientific Study Project for institutes of Higher Learning,Ministry of Education,Liaoning Province[LJKMZ20220673]+2 种基金the Project supported by the State Key Laboratory of Geodesy and Earths'Dynamics,Innovation Academy for Precision Measurement Science and Technology[SKLGED2023-3-2]Liaoning Revitalization Talent Program[XLYC2203162]Natural Science Foundation of Hebei Province in China[D2023402024].
文摘Zenith wet delay(ZWD)is a key parameter for the precise positioning of global navigation satellite systems(GNSS)and occupies a central role in meteorological research.Currently,most models only consider the periodic variability of the ZWD,neglecting the effect of nonlinear factors on the ZWD estimation.This oversight results in a limited capability to reflect the rapid fluctuations of the ZWD.To more accurately capture and predict complicated variations in ZWD,this paper developed the CRZWD model by a combination of the GPT3 model and random forests(RF)algorithm using 5-year atmospheric profiles from 70 radiosonde(RS)stations across China.Taking the external 25 test stations data as reference,the root mean square(RMS)of the CRZWD model is 29.95 mm.Compared with the GPT3 model and another model using backpropagation neural network(BPNN),the accuracy has improved by 24.7%and 15.9%,respectively.Notably,over 56%of the test stations exhibit an improvement of more than 20%in contrast to GPT3-ZWD.Further temporal and spatial characteristic analyses also demonstrate the significant accuracy and stability advantages of the CRZWD model,indicating the potential prospects for GNSS-based applications.
基金supported by the Fundacao para a Ciencia e Tecnologia,FCT,under the project https://doi.org/10.54499/UIDB/04674/2020(accessed on 1 January 2025).
文摘In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.
基金the National Natural Science Foundation of China(U22A20314,82470988,32070826)National Key R&D of Program of China(2022YFC2504201)+2 种基金Outstanding Youth Fund of Chongqing Natural Science Foundation(CSTB2023NSCQJQX0006)Science and Technology Research Project of Chongqing Education Commission(KJQN202200471)CQMU Program for Youth Innovation in Future Medicine(W0075).
文摘The repair of the periodontal membrane is essential for the successful management of periodontal disease and dental trauma.Emdogain®(EMD)is widely used in periodontal therapy due to its ability to promote repair.Despite substantial research,the cellular and molecular mechanisms underlying EMD’s effects,particularly at the single-cell resolution,remain incompletely understood.This study established a delayed tooth replantation model in rats to investigate these aspects.Tooth loss rate and degree of loosening were evaluated at 4 and 8 weeks.Micro-CT,HE staining,TRAP staining,and immunofluorescence staining were evaluated to assess EMD’s efficacy.Single-cell sequencing analyses generated single-cell maps that explored enrichment pathways,cell communication,and potential repair mechanisms.Findings indicated that EMD could reduce the rate of tooth loss,promote periodontal membrane repair,and reduce root and bone resorption.Single-cell analysis revealed that EMD promotes the importance of Vtn+fibroblasts,enhancing matrix and tissue regeneration functions.Additionally,EMD stimulated osteogenic pathways,reduced osteoclastic activity,and promoted angiogenesis-related pathways,particularly bone-related H-type vessel expression in endothelial cells.Gene modules associated with angiogenesis,osteogenesis,and odontoblast differentiation were identified,suggesting EMD might facilitate osteogenesis and odontoblast differentiation by upregulating endothelium-related genes.Immune cell analysis indicated that EMD did not elicit a significant immune response.Cell communication analysis suggested that EMD fostered pro-regenerative networks driven by interactions between mesenchymal stem cells,fibroblasts,and endothelial cells.In conclusion,EMD proves to be an effective root surface therapy agent that supports the restoration of delayed replantation teeth.
文摘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.
基金supported by Prince Sultan University through TAS research lab。
文摘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.
基金supported by the Science and Technology Research Project(KJQN202212805)of the Chongqing Education Commissionthe Special Funding Project(2021XJS08)of Army Medical University。
文摘Background:Paraplegia after spinal cord ischemia is a devastating condition in the clinic.Here,we develop an awake rabbit model of spinal cord ischemia with delayed paraplegia and explore the influence of ambient temperature on the outcomes after injury.Methods:A total of 47 male rabbits were involved in the present study.Transient spinal cord ischemia was induced by occluding the infrarenal abdominal aorta of awake rabbits at different ambient temperatures.To find the optimal conditions for developing delayed paraplegia,hindlimb motor function after ischemia was evaluated between experiments.Results:The onset and magnitude of ischemic injury varied with the ambient temperature maintained during the peri-i schemia period.More serious spinal cord injury occurred when ischemia was induced at higher temperatures.At 18°C,25-minute ischemia resulted in 74%of rabbits developing delayed paraplegia.At a temperature of 28°C or higher,most of the animals developed acute paraplegia immediately.While at 13°C,rabbits usually regained normal motor function without paraplegia.Conclusion:This awake rabbit model is highly reproducible and will be helpful in future studies of delayed paraplegia after spinal cord ischemia.The ambient temperature must be considered while using this model during investigation of therapeutic interventions.
基金Deanship of Research and Graduate Studies at King Khalid University for funding this work through large Research Project under Grant Number RGP2/302/45supported by the Deanship of Scientific Research,Vice Presidency forGraduate Studies and Scientific Research,King Faisal University,Saudi Arabia(Grant Number A426).
文摘Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.
文摘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 R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.
文摘Delayed coking is an important process consumption and light oil yield are important factors used to convert heavy oils to light products. Energy for evaluating the delayed coking process. This paper analyzes the energy consumption and product yields of delayed coking units in China. The average energy consumption shows a decreasing trend in recent years. The energy consumption of different refineries varies greatly, with the average value of the highest energy consumption approximately twice that of the lowest energy consumption. The factors affecting both energy consumption and product yields were analyzed, and correlation models of energy consumption and product yields were established using a quadratic polynomial. The model coefficients were calculated through least square regression of collected industrial data of delayed coking units. Both models showed good calculation accuracy. The average absolute error of the energy consumption model was approximately 85 MJ/t, and that of the product yield model ranged from 1 wt% to 2.3 wt%. The model prediction showed that a large annual processing capacity and high load rate will result in a reduction in energy consumption.
文摘Mathematical delay modelling has a significant role in the different disciplines such as behavioural,social,physical,biological engineering,and bio-mathematical sciences.The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus(COVID-19).Due to the unavailability of vaccines for the coronavirus worldwide,delay factors such as social distance,quarantine,travel restrictions,extended holidays,hospitalization,and isolation have contributed to controlling the coronavirus epidemic.We have analysed the reproduction number and its sensitivity to parameters.If,R_(covid)>1then this situation will help to eradicate the disease and if,R_(covid)>1 the virus will spread rapidly in the human beings.Well-known theorems such as Routh Hurwitz criteria and Lasalle invariance principle have presented for stability.The local and global stabilizes for both equilibria of the model have also been presented.Also,we have analysed the effect of delay reason on the reproduction number.In the last,some very useful numerical consequences have presented in support of hypothetical analysis.
基金supported by the National Natural Science Foundation of China (Grant No 70571017)the Research Foundation from Provincial Education Department of Zhejiang of China (Grant No 21186000507)
文摘Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue length is investigated in detail. The main advantage of the new model is that its stability domain is larger even without an extra controller. By linear stability analysis and numerical simulation, tbe effectiveness and feasibility of the novel model in internet congestion control are verified.
文摘The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix(HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.
文摘In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.
基金supported by the National Natural Science Foundation of China(42204022,52174160,52274169)Open Fund of Hubei Luojia Laboratory(230100031)+2 种基金the Open Fund of State Laboratory of Information Engineering in Surveying,Mapping and Remote Sensing,Wuhan University(23P02)the Fundamental Research Funds for the Central Universities(2023ZKPYDC10)China University of Mining and Technology-Beijing Innovation Training Program for College Students(202302014,202202023)。
文摘The precise correction of atmospheric zenith tropospheric delay(ZTD)is significant for the Global Navigation Satellite System(GNSS)performance regarding positioning accuracy and convergence time.In the past decades,many empirical ZTD models based on whether the gridded or scattered ZTD products have been proposed and widely used in the GNSS positioning applications.But there is no comprehensive evaluation of these models for the whole China region,which features complicated topography and climate.In this study,we completely assess the typical empirical models,the IGGtropSH model(gridded,non-meteorology),the SHAtropE model(scattered,non-meteorology),and the GPT3 model(gridded,meteorology)using the Crustal Movement Observation Network of China(CMONOC)network.In general,the results show that the three models share consistent performance with RMSE/bias of 37.45/1.63,37.13/2.20,and 38.27/1.34 mm for the GPT3,SHAtropE and IGGtropSH model,respectively.However,the models had a distinct performance regarding geographical distribution,elevation,seasonal variations,and daily variation.In the southeastern region of China,RMSE values are around 50 mm,which are much higher than that in the western region,approximately 20 mm.The SHAtropE model exhibits better performance for areas with large variations in elevation.The GPT3 model and the IGGtropSH model are more stable across different months,and the SHAtropE model based on the GNSS data exhibits superior performance across various UTC epochs.
基金supported by the Brain Korea 21 PLUS Project,National Research Foundation of Korea(NRF-2013R1A2A2A01068127NRF-2013R1A1A2A10009458)Jiangsu Province University Natural Science Research Project(13KJB510003)
文摘The performance of the model algorithm control method is partially based on the accuracy of the system＇s model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. Neural networks have the ability to ＂learn＂the characteristics of a system through nonlinear mapping to represent nonlinear functions as well as their inverse functions. This paper presents a model algorithm control method using neural networks for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one produces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to illustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.
文摘Through the study,the nonlinear delayed modelling has vital significance in the different field of allied sciences like computational biology,computational chemistry,computational physics,computational economics and many more.Polio is a contagious viral illness that in its most severe form causes nerve injury leading to paralysis,difficulty breathing and sometimes death.In recent years,developing regions like Asia,Africa and sub-continents facing a dreadful situation of poliovirus.That is the reason we focus on the treatment of the polio epidemic model with different delay strategies in this article.Polio delayed epidemic model is categorized into four compartments like susceptible,exposed,infective and vaccinated classes.The equilibria,positivity,boundedness,and reproduction number are investigated.Also,the sensitivity of the parameters is analyzed.Well,known results like the Routh Hurwitz criterion and Lyapunov function stabilities are investigated for polio delayed epidemic model in the sense of local and global respectively.Furthermore,the computer simulations are presented with different traditions in the support of the analytical analysis of the polio delayed epidemic model.
