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
Background:Maternal mortality is a prevalent issue in healthcare provision worldwide.It is particularly common in developing and underdeveloped countries,where maternal deaths during childbirth or pregnancy occur freq...Background:Maternal mortality is a prevalent issue in healthcare provision worldwide.It is particularly common in developing and underdeveloped countries,where maternal deaths during childbirth or pregnancy occur frequently.Various internal and external factors contribute to the high maternal mortality rate in specific regions.One model,known as the three delays model approach,examines three distinct causes that contribute to this problem.The first delay is the lack of awareness in seeking timely healthcare,the second delay involves obstacles in reaching healthcare facilities on time,and the third delay relates to poor or inadequate healthcare provision in tertiary care facilities.These delays are responsible for the elevated maternal mortality rates,with the prevalence of each delay varying across regions.Objective:The objective of this literature review is to examine and critically evaluate existing literature on perceptions and investigations regarding maternal mortality in Southeast Asia,Europe and Africa,utilizing the three delays model approach as a categorization framework.Method:This literature review followed BEME guide No.3.A total of 18 articles were included in the sample after conducting a thorough search of various databases and search engines.A Prisma flowchart was created,and the articles were critically appraised.Results:A total of 18 articles focusing on different regions were analyzed.The findings revealed that in countries of Southeast Asia,the primary cause of maternal mortality is the first delay,which refers to the lack of awareness in seeking medical care.On the other hand,in Africa and other European countries,the second and third delays are more prominently associated with maternal mortality.Conclusion:Inadequate care is one of the major causes of maternal mortality in majority of regions acrossthe globe.Multiple factors can hinder access to appropriate healthcare.The three delays model plays a significant role in the higher maternal mortality rate.By raising awareness among women and their families about the importance of seeking healthcare,the risk of fatality can be reduced.Similarly,in developing regions,it is crucial to ensure that healthcare facilities are easily accessible and provide high-quality emergency obstetric care to meet the needs of pregnant women in critical situations.展开更多
A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-la...A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-latitude wind field, and the physical meaning of the corresponding solution is also discussed.展开更多
In this manuscript,the mathematical analysis of corona virus model with time delay effect is studied.Mathematical modelling of infectious diseases has substantial role in the different disciplines such as biological,e...In this manuscript,the mathematical analysis of corona virus model with time delay effect is studied.Mathematical modelling of infectious diseases has substantial role in the different disciplines such as biological,engineering,physical,social,behavioural problems and many more.Most of infectious diseases are dreadful such as HIV/AIDS,Hepatitis and 2019-nCov.Unfortunately,due to the non-availability of vaccine for 2019-nCov around the world,the delay factors like,social distancing,quarantine,travel restrictions,holidays extension,hospitalization and isolation are used as key tools to control the pandemic of 2019-nCov.We have analysed the reproduction number𝐑𝐑𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧of delayed model.Two key strategies from the reproduction number of 2019-nCov model,may be followed,according to the nature of the disease as if it is diminished or present in the community.The more delaying tactics eventually,led to the control of pandemic.Local and global stability of 2019-nCov model is presented for the strategies.We have also investigated the effect of delay factor on reproduction number𝐑R_(nCov).Finally,some very useful numerical results are presented to support the theoretical analysis of the model.展开更多
Chronic hepatitis B infection is a major health problem,with approximately 350 million virus carriers worldwide.In Africa,about 30%-60% of children and 60%-100% of adults have
In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the lin...In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.展开更多
Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural birth...Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.展开更多
In 2020,the reported cases were 0.12 million in the six regions to the official report of the World Health Organization(WHO).For most children infected with leprosy,0.008629 million cases were detected under fifteen.T...In 2020,the reported cases were 0.12 million in the six regions to the official report of the World Health Organization(WHO).For most children infected with leprosy,0.008629 million cases were detected under fifteen.The total infected ratio of the children population is approximately 4.4 million.Due to theCOVID-19 pandemic,the awareness programs implementation has been disturbed.Leprosy disease still has a threat and puts people in danger.Nonlinear delayed modeling is critical in various allied sciences,including computational biology,computational chemistry,computational physics,and computational economics,to name a few.The time delay effect in treating leprosy delayed epidemic model is investigated.The whole population is divided into four groups:those who are susceptible,those who have been exposed,those who have been infected,and those who have been vaccinated.The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven.The parameters’sensitivity is also examined.The analytical analysis is supported by computer results that are presented in a variety of ways.The proposed approach in this paper preserves equilibrium points and their stabilities,the existence and uniqueness of solutions,and the computational ease of implementation.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
The classical autoregressive(AR)model has been widely applied to predict future data usingmpast observations over five decades.As the classical AR model required m unknown parameters,this paper implements the AR model...The classical autoregressive(AR)model has been widely applied to predict future data usingmpast observations over five decades.As the classical AR model required m unknown parameters,this paper implements the AR model by reducing m parameters to two parameters to obtain a new model with an optimal delay called as the m-delay AR model.We derive the m-delay AR formula for approximating two unknown parameters based on the least squares method and develop an algorithm to determine optimal delay based on a brute-force technique.The performance of them-delay AR model was tested by comparing with the classical AR model.The results,obtained from Monte Carlo simulation using the monthly mean minimum temperature in PerthWestern Australia from the Bureau of Meteorology,are no significant difference compared to those obtained from the classical AR model.This confirms that the m-delay AR model is an effective model for time series analysis.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
Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence ...Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced.According to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the model.We illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.展开更多
We develop an interconnect crosstalk estimation model on the assumption of linearity for CMOS device. First, we analyze the terminal response of RC model on the worst condition from theS field to the time domain. The ...We develop an interconnect crosstalk estimation model on the assumption of linearity for CMOS device. First, we analyze the terminal response of RC model on the worst condition from theS field to the time domain. The exact 3 order coefficients inS field are obtained due to the interconnect tree model. Based on this, a crosstalk peak estimation formula is presented. Unlike other crosstalk equations in the literature, this formula is only used coupled capacitance and grand capacitance as parameter. Experimental results show that, compared with the SPICE results, the estimation formulae are simple and accurate. So the model is expected to be used in such fields as layout-driven logic and high level synthesis, performance-driven floorplanning and interconnect planning.展开更多
A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensur...A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.展开更多
To design and evaluate vehicle-to-vehicle(V2V)communication systems in intelligent transportation system(ITS),it is important to understand the propagation mechanisms and channel models of V2V channels.This paper aims...To design and evaluate vehicle-to-vehicle(V2V)communication systems in intelligent transportation system(ITS),it is important to understand the propagation mechanisms and channel models of V2V channels.This paper aims to analyze the channel models at 5.2 GHz for the highway environment in obstructed line-of-sight(OLoS)and line-of-sight(LoS)scenarios,particularly the vehicle connectivity probability derivation based on the propagation model obtained from measurement.First,the path loss(PL),shadow fading(SF),narrowband K-factor,and small-scale amplitude fading are analyzed.Results showed that the received signal magnitude follows Rice and Weibull distribution in LoS and OLoS scenarios,respectively.Second,we develop simple and low-complexity tapped delay line(TDL)models with a 10 MHz bandwidth for LoS and OLoS scenarios;in addition,we investigate the wideband K-factor,the root mean square delay spread(RMS-DS),and delay-Doppler spectrum.Third,we derive the closed form connectivity probability between any two vehicles in the presence of Weibull fading channel,and analyze the effects of Weibull fading channel and traffic parameters on connectivity.It is found that Weibull fading parameter,transmit power and vehicle density have positive impact on connectivity probability,PL exponent has negative impact on connectivity probability.展开更多
The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator system.The delay differential models are very significant and always difficult to solve the dyn...The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator system.The delay differential models are very significant and always difficult to solve the dynamical kind of ecological nonlinear two-prey and one-predator system.Therefore,a stochastic numerical paradigm based artificial neural network(ANN)along with the Levenberg-Marquardt backpropagation(L-MB)neural networks(NNs),i.e.,L-MBNNs is proposed to solve the dynamical twoprey and one-predator model.Three different cases based on the dynamical two-prey and one-predator system have been discussed to check the correctness of the L-MBNNs.The statistic measures of these outcomes of the dynamical two-prey and one-predator model are chosen as 13%for testing,12%for authorization and 75%for training.The exactness of the proposed results of L-MBNNs approach for solving the dynamical two-prey and onepredator model is observed with the comparison of the Runge-Kutta method with absolute error ranges between 10−05 to 10−07.To check the validation,constancy,validity,exactness,competence of the L-MBNNs,the obtained state transitions(STs),regression actions,correlation presentations,MSE and error histograms(EHs)are also provided.展开更多
Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to...Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.展开更多
Delay considerttion has been a major issue in design and test of high performance digital circuits . The assumption of input signal change occurring only when all internal nodes are stable restricts the increase of cl...Delay considerttion has been a major issue in design and test of high performance digital circuits . The assumption of input signal change occurring only when all internal nodes are stable restricts the increase of clock frequency. It is no longer true for wave pipelining circuits. However, previous logical delay models are based on the assumption. In addition, the stable time of a robust delay test generally depends on the longest sensitizable path delay. Thus , a new delay model is desirable. This paper explores the necessity first. Then, Boolean process to analytically describe the logical and timing behavior of a digital circuit is reviewed . The concept of sensitization is redefined precisely in this paper. Based on the new concept of sensitization, an analytical delay model is introduced . As a result , many untestable delay faults under the logical delay model can be tested if the output waveforms can be sampled at more time points. The longest sensitiaable path length is computed for circuit design and delay test .展开更多
By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r &l...By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r <SUB>1</SUB> and r <SUB>2</SUB> are continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞) with are positive continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞), b <SUB>i </SUB>(i = 1, 2) is nonnegative continuous ω-periodic function in R <SUB>+</SUB> = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.展开更多
To achieve a characterization method for the gate delay library used in block based statistical static timing analysis with neither unacceptably poor accuracy nor forbiddingly high cost,we found that general-purpose g...To achieve a characterization method for the gate delay library used in block based statistical static timing analysis with neither unacceptably poor accuracy nor forbiddingly high cost,we found that general-purpose gate delay models are useful as intermediaries between the circuit simulation data and the gate delay models in required forms.In this work,two gate delay models for process variation considering different driving and loading conditions are proposed.From the testing results,these two models,especially the one that combines effective dimension reduction(EDR) from statistics society with comprehensive gate delay models,offer good accuracy with low characterization cost,and they are thus competent for use in statistical timing analysis(SSTA).In addition, these two models have their own value in other SSTA techniques.展开更多
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Background:Maternal mortality is a prevalent issue in healthcare provision worldwide.It is particularly common in developing and underdeveloped countries,where maternal deaths during childbirth or pregnancy occur frequently.Various internal and external factors contribute to the high maternal mortality rate in specific regions.One model,known as the three delays model approach,examines three distinct causes that contribute to this problem.The first delay is the lack of awareness in seeking timely healthcare,the second delay involves obstacles in reaching healthcare facilities on time,and the third delay relates to poor or inadequate healthcare provision in tertiary care facilities.These delays are responsible for the elevated maternal mortality rates,with the prevalence of each delay varying across regions.Objective:The objective of this literature review is to examine and critically evaluate existing literature on perceptions and investigations regarding maternal mortality in Southeast Asia,Europe and Africa,utilizing the three delays model approach as a categorization framework.Method:This literature review followed BEME guide No.3.A total of 18 articles were included in the sample after conducting a thorough search of various databases and search engines.A Prisma flowchart was created,and the articles were critically appraised.Results:A total of 18 articles focusing on different regions were analyzed.The findings revealed that in countries of Southeast Asia,the primary cause of maternal mortality is the first delay,which refers to the lack of awareness in seeking medical care.On the other hand,in Africa and other European countries,the second and third delays are more prominently associated with maternal mortality.Conclusion:Inadequate care is one of the major causes of maternal mortality in majority of regions acrossthe globe.Multiple factors can hinder access to appropriate healthcare.The three delays model plays a significant role in the higher maternal mortality rate.By raising awareness among women and their families about the importance of seeking healthcare,the risk of fatality can be reduced.Similarly,in developing regions,it is crucial to ensure that healthcare facilities are easily accessible and provide high-quality emergency obstetric care to meet the needs of pregnant women in critical situations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11202106 and 61302188)the Specialized Research Fund for the Doctoral Program of Higher Education,China(Grant No.20123228120005)+2 种基金the Fund from the Jiangsu Sensor Network and Modern Meteorological Equipment Preponderant Discipline Platform,Chinathe Natural Science Fundation from the Universities of Jiangsu Province,China(Grant No.13KJB170016)the Advance Research Foundation in NUIST of China(Grant Nos.20110371 and 20110385)
文摘A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-latitude wind field, and the physical meaning of the corresponding solution is also discussed.
文摘In this manuscript,the mathematical analysis of corona virus model with time delay effect is studied.Mathematical modelling of infectious diseases has substantial role in the different disciplines such as biological,engineering,physical,social,behavioural problems and many more.Most of infectious diseases are dreadful such as HIV/AIDS,Hepatitis and 2019-nCov.Unfortunately,due to the non-availability of vaccine for 2019-nCov around the world,the delay factors like,social distancing,quarantine,travel restrictions,holidays extension,hospitalization and isolation are used as key tools to control the pandemic of 2019-nCov.We have analysed the reproduction number𝐑𝐑𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧of delayed model.Two key strategies from the reproduction number of 2019-nCov model,may be followed,according to the nature of the disease as if it is diminished or present in the community.The more delaying tactics eventually,led to the control of pandemic.Local and global stability of 2019-nCov model is presented for the strategies.We have also investigated the effect of delay factor on reproduction number𝐑R_(nCov).Finally,some very useful numerical results are presented to support the theoretical analysis of the model.
基金supported by the National Natural Science Foundationof China,No.60774036the NSF of Hubei Province 2008CDA063
文摘Chronic hepatitis B infection is a major health problem,with approximately 350 million virus carriers worldwide.In Africa,about 30%-60% of children and 60%-100% of adults have
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61272069,61272114,61073026,61170031,and 61100076)
文摘In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.
文摘Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.
文摘In 2020,the reported cases were 0.12 million in the six regions to the official report of the World Health Organization(WHO).For most children infected with leprosy,0.008629 million cases were detected under fifteen.The total infected ratio of the children population is approximately 4.4 million.Due to theCOVID-19 pandemic,the awareness programs implementation has been disturbed.Leprosy disease still has a threat and puts people in danger.Nonlinear delayed modeling is critical in various allied sciences,including computational biology,computational chemistry,computational physics,and computational economics,to name a few.The time delay effect in treating leprosy delayed epidemic model is investigated.The whole population is divided into four groups:those who are susceptible,those who have been exposed,those who have been infected,and those who have been vaccinated.The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven.The parameters’sensitivity is also examined.The analytical analysis is supported by computer results that are presented in a variety of ways.The proposed approach in this paper preserves equilibrium points and their stabilities,the existence and uniqueness of solutions,and the computational ease of implementation.
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.
文摘The classical autoregressive(AR)model has been widely applied to predict future data usingmpast observations over five decades.As the classical AR model required m unknown parameters,this paper implements the AR model by reducing m parameters to two parameters to obtain a new model with an optimal delay called as the m-delay AR model.We derive the m-delay AR formula for approximating two unknown parameters based on the least squares method and develop an algorithm to determine optimal delay based on a brute-force technique.The performance of them-delay AR model was tested by comparing with the classical AR model.The results,obtained from Monte Carlo simulation using the monthly mean minimum temperature in PerthWestern Australia from the Bureau of Meteorology,are no significant difference compared to those obtained from the classical AR model.This confirms that the m-delay AR model is an effective model for time series analysis.
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 Natural Science Foundation of Shanxi Province(202303021211003)the National Natural Science Foundation of China(12126349,11601293,12361102)the Scientific Plan of Guizhou Province(No.Qian Ke He Jichu-ZK[2021]YiBan002).
文摘Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced.According to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the model.We illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.
基金SupportedbytheNationalHighTechnologyResearchandDevelopmentProgramofChina (863Plan) (863 SOC Y 3 3 2 )
文摘We develop an interconnect crosstalk estimation model on the assumption of linearity for CMOS device. First, we analyze the terminal response of RC model on the worst condition from theS field to the time domain. The exact 3 order coefficients inS field are obtained due to the interconnect tree model. Based on this, a crosstalk peak estimation formula is presented. Unlike other crosstalk equations in the literature, this formula is only used coupled capacitance and grand capacitance as parameter. Experimental results show that, compared with the SPICE results, the estimation formulae are simple and accurate. So the model is expected to be used in such fields as layout-driven logic and high level synthesis, performance-driven floorplanning and interconnect planning.
基金supported by the National High Technology Research and Development Program of China(863)(511-0910-1031)the National"10th Five-Year"Science and Technique Important Program of China(2002BA404A07)
文摘A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.
基金supported by the National Natural Science Foundation of China(No.61871059)Scientific Innovation Practice Project of Postgraduates of Chang’an University(No.300103722006).
文摘To design and evaluate vehicle-to-vehicle(V2V)communication systems in intelligent transportation system(ITS),it is important to understand the propagation mechanisms and channel models of V2V channels.This paper aims to analyze the channel models at 5.2 GHz for the highway environment in obstructed line-of-sight(OLoS)and line-of-sight(LoS)scenarios,particularly the vehicle connectivity probability derivation based on the propagation model obtained from measurement.First,the path loss(PL),shadow fading(SF),narrowband K-factor,and small-scale amplitude fading are analyzed.Results showed that the received signal magnitude follows Rice and Weibull distribution in LoS and OLoS scenarios,respectively.Second,we develop simple and low-complexity tapped delay line(TDL)models with a 10 MHz bandwidth for LoS and OLoS scenarios;in addition,we investigate the wideband K-factor,the root mean square delay spread(RMS-DS),and delay-Doppler spectrum.Third,we derive the closed form connectivity probability between any two vehicles in the presence of Weibull fading channel,and analyze the effects of Weibull fading channel and traffic parameters on connectivity.It is found that Weibull fading parameter,transmit power and vehicle density have positive impact on connectivity probability,PL exponent has negative impact on connectivity probability.
基金This research received funding support from the NSRF via the Program Management Unit for Human Resources&Institutional Development,Research and Innovation(grant number B05F640088).
文摘The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator system.The delay differential models are very significant and always difficult to solve the dynamical kind of ecological nonlinear two-prey and one-predator system.Therefore,a stochastic numerical paradigm based artificial neural network(ANN)along with the Levenberg-Marquardt backpropagation(L-MB)neural networks(NNs),i.e.,L-MBNNs is proposed to solve the dynamical twoprey and one-predator model.Three different cases based on the dynamical two-prey and one-predator system have been discussed to check the correctness of the L-MBNNs.The statistic measures of these outcomes of the dynamical two-prey and one-predator model are chosen as 13%for testing,12%for authorization and 75%for training.The exactness of the proposed results of L-MBNNs approach for solving the dynamical two-prey and onepredator model is observed with the comparison of the Runge-Kutta method with absolute error ranges between 10−05 to 10−07.To check the validation,constancy,validity,exactness,competence of the L-MBNNs,the obtained state transitions(STs),regression actions,correlation presentations,MSE and error histograms(EHs)are also provided.
基金Supported by the Science Foundation of Educational Committee of Hunan Province
文摘Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.
文摘Delay considerttion has been a major issue in design and test of high performance digital circuits . The assumption of input signal change occurring only when all internal nodes are stable restricts the increase of clock frequency. It is no longer true for wave pipelining circuits. However, previous logical delay models are based on the assumption. In addition, the stable time of a robust delay test generally depends on the longest sensitizable path delay. Thus , a new delay model is desirable. This paper explores the necessity first. Then, Boolean process to analytically describe the logical and timing behavior of a digital circuit is reviewed . The concept of sensitization is redefined precisely in this paper. Based on the new concept of sensitization, an analytical delay model is introduced . As a result , many untestable delay faults under the logical delay model can be tested if the output waveforms can be sampled at more time points. The longest sensitiaable path length is computed for circuit design and delay test .
基金National Natural Science Foundation of China (Grant No.10071022)Mathematical Tianyuan Foudation of China (Grant No.TY10026002-01-05-03) & Shanghai Priority Academic Research.
文摘By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r <SUB>1</SUB> and r <SUB>2</SUB> are continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞) with are positive continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞), b <SUB>i </SUB>(i = 1, 2) is nonnegative continuous ω-periodic function in R <SUB>+</SUB> = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.
文摘To achieve a characterization method for the gate delay library used in block based statistical static timing analysis with neither unacceptably poor accuracy nor forbiddingly high cost,we found that general-purpose gate delay models are useful as intermediaries between the circuit simulation data and the gate delay models in required forms.In this work,two gate delay models for process variation considering different driving and loading conditions are proposed.From the testing results,these two models,especially the one that combines effective dimension reduction(EDR) from statistics society with comprehensive gate delay models,offer good accuracy with low characterization cost,and they are thus competent for use in statistical timing analysis(SSTA).In addition, these two models have their own value in other SSTA techniques.