The increasing demand due to development and advancement in every field of life has caused the depletion of fossil fuels.This depleting fossil fuel reserve throughout the world has enforced to get energy from alternat...The increasing demand due to development and advancement in every field of life has caused the depletion of fossil fuels.This depleting fossil fuel reserve throughout the world has enforced to get energy from alternative/renewable sources.One of the economicalways to get energy is through the utilization of solar ponds.In this study,a mathematical model of a salt gradient solar pond under the Islamabad climatic conditions has been analyzed for the first time.The model uses a one-dimensional finite difference explicit method for optimization of different zone thicknesses.The model depicts that NCZ(Non-Convective Zone)thickness has a significant effect on LCZ(Lower Convective Zone)temperature and should be kept less than 1.7mfor the optimal temperature.It is also observed that for long-termoperation of a solar pond,heat should be extracted by keeping the mass flowrate of 17.3 kg/m^(2)/day.Themodel also suggests that when the bottom reflectivity is about 0.3,then only 24%of the radiation is absorbed in the pond.展开更多
The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displa...The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.展开更多
We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equation...We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.展开更多
Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.Thi...Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.展开更多
In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to...In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to challenges,particularly concerning housing prices,which have drawn widespread societal attention.This article explores the theories of housing prices,analyzes factors influencing them,and conducts an empirical investigation of the impact of representative factors on ordinary residential prices.Using regression analysis and the entropy weight method,a mathematical model was developed to examine how various factors affect housing prices.展开更多
Extensive historical data of a sewage treatment works are required by numerical models in order to simulate the biological processes accurately. However, the data are recorded mostly for daily operational purpose. The...Extensive historical data of a sewage treatment works are required by numerical models in order to simulate the biological processes accurately. However, the data are recorded mostly for daily operational purpose. They are basically not comprehensive enough to meet the modelling’s requirements. A comprehensive sampling protocol to accurately characterise the influent is required in order to determine all model components, which is very time-consuming and expensive. In a project of evaluating a sewage treatment works in Chongqing by using BioWin 4.1 for mathematical modelling, sensitivity analysis was conducted to determine the most critical parameters for process monitoring. It was found that influent characteristics, wasted sludge flow rate, water temperatures, DO levels of the biological tanks and five bio-kinetic parameters were the most influential parameters governing the plant performance. Therefore, apart from monitoring the effluent quality, regular checking of the afore-mentioned influential parameters can help examine the performance of a sewage treatment works. Moreover, operators of the sewage treatment works can conduct “what-if” analysis to determine how these most influential parameters can be adjusted to improve the treatment performance of the sewage treatment works.展开更多
A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten ki...A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten kinetics. Analytical expression pertaining to the substrate concentration was reported for all possible values of Thiele module φ and α . In this work, we report the theoretically evaluated steady-state effectiveness factor for immobilized enzyme systems in porous spherical particles. These analytical results were found to be in good agreement with numerical results. Moreover, herein we employ new “Homotopy analysis method” (HAM) to solve non-linear reaction/diffusion equation.展开更多
Objective： The progression of human cancer is characterized by the accumulation of genetic instability. An increasing number of experimental genetic molecular techniques have been used to detect chromosome aberration...Objective： The progression of human cancer is characterized by the accumulation of genetic instability. An increasing number of experimental genetic molecular techniques have been used to detect chromosome aberrations. Previous studies on chromosome abnormalities often focused on identifying the frequent loci of chromosome alterations, but rarely addressed the issue of interrelationship of chromosomal abnormalities. In the last few years, several mathematical models have been employed to construct models of carcinogenesis, in an attempt to identify the time order and cause-and-effect relationship of chromosome aberrations. The principles and applications of these models are reviewed and compared in this paper. Mathematical modeling of carcinogenesis can contribute to our understanding of the molecular genetics of tumor development, and identification of cancer related genes, thus leading to improved clinical practice of cancer.展开更多
The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal...The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.展开更多
In this paper,we developed a mathematical model for Streptococcus suis,which is an epidemic by considering the moisture that affects the infection.The disease is caused by Streptococcus suis infection found in pigs wh...In this paper,we developed a mathematical model for Streptococcus suis,which is an epidemic by considering the moisture that affects the infection.The disease is caused by Streptococcus suis infection found in pigs which can be transmitted to humans.The patients of Streptococcus suis were generally found in adults males and the elderly who contacted pigs or who ate uncooked pork.In human cases,the infection can cause a severe illness and death.This disease has an impact to the financial losses in the swine industry.In the development of models for this disease,we have divided the population into 7 related groups which are susceptible pig compartment,infected pig compartment,quarantined pig compartment,recovered pig compartment,susceptible human compartment,infected human compartment,and recovered human compartment.After that,we use this model and a quarantine strategy to analyze the spread of the infection.In addition,the basic reproduction number R0 is determined by using the next-generation matrix which can analyze the stability of the model.The numerical simulations of the proposed model are illustrated to confirm the results from theorems.The results showed that there is an effect from moisture to the disease transmission.When the moisture increases the disease infection also increases.展开更多
Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a ...Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories.Mathematicalmodels play an important role in the diagnosis and treatment of cancer.In this study,data of 42 BI-RADS 4 patients taken fromthe Center for Breast Health,Near East University Hospital is utilized.Regarding the analysis,a mathematical model is constructed by dividing the population into 4 compartments.Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk.Numerical simulations of the parameters are demonstrated.The results of the model have revealed that an increase in the lactation rate and earlymenopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age,the palpable mass,and family history is distinctive.Furthermore,the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined.Consequently,the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories.All things considered,with the assistance of the most effective parameters,the range of cancer risks in BI-RADS 4 subcategories will decrease.展开更多
A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The m...A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.展开更多
Environmental conscious manufacturing has become an important issue in industry because of market pressure and environmental regulations. An environmental risk assessment model was developed based on the network analy...Environmental conscious manufacturing has become an important issue in industry because of market pressure and environmental regulations. An environmental risk assessment model was developed based on the network analytic method and fuzzy set theory. The "interval analysis method" was applied to deal with the on site monitoring data as basic information for assessment. In addition, the fuzzy set theory was employed to allow uncertain, interactive and dynamic information to be effectively incorporated into the environmental risk assessment. This model is a simple, practical and effective tool for evaluating the environmental risk of manufacturing industry and for analyzing the relative impacts of emission wastes, which are hazardous to both human and ecosystem health. Furthermore, the model is considered useful for design engineers and decision maker to design and select processes when the costs, environmental impacts and performances of a product are taken into consideration.展开更多
On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in...On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.展开更多
Meningococcal meningitis(MCM)is one of the serious public health threats in the tropical and sub-tropical regions.In this paper,we propose an epidemic model to study the transmission dynamics of MCM with high-and low-...Meningococcal meningitis(MCM)is one of the serious public health threats in the tropical and sub-tropical regions.In this paper,we propose an epidemic model to study the transmission dynamics of MCM with high-and low-risk susceptible populations.The model considers two different groups of susceptible individuals depending on the availability of medical resources(MR,including hospitals,health workers,etc.),which varies the infection risk.We find that the model exhibits the phenomenon of backward bifurcation(BB),which increases the difficulty of MCM control since the dynamics are not merely relying on the basic reproduction number,TZo.This study explores the effects of MR on the MCM epidemics by mathematical analysis and shows the existence of BB on MCM disease.Our findings suggest that providing adequate MR in a community is crucial in mitigating MCM incidences and deaths,especially,in the MCM endemic regions.展开更多
In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are...In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are also considered.in particular,the conditions for the existence of Hopf bifurcation can be given in terms of the coefficients of the characteristic equation.The method extends the application of the Hopf bifurcation theorem to higher differential equations which occur in biological models,chemical models,and epidemiological models etc.展开更多
Time-limited dispatching(TLD)analysis of the full authority digital engine control(FADEC)systems is an important part of the aircraft system safety analysis and a necessary task for the certification of commercial air...Time-limited dispatching(TLD)analysis of the full authority digital engine control(FADEC)systems is an important part of the aircraft system safety analysis and a necessary task for the certification of commercial aircraft and aeroengines.In the time limited dispatch guidance document ARP5107B,a single-fault Markov model(MM)approach is proposed for TLD analysis.However,ARP5107B also requires that the loss of thrust control(LOTC)rate error calculated by applying the single-fault MM must be less than 5%when performing airworthiness certification.Firstly,the sources of accuracy errors in three kinds of MM are analyzed and specified through a case study of the general FADEC system,and secondly a two-fault MM considering maintenance policy is established through analyzing and calculating the expected repair time when two related faults happen.Finally,a specific FADEC system is given to study on the influence factors of accuracy error in the single-fault MM,and the results show that the accuracy error of the single-fault MM decreases with the increase of short or long prescribed dispatch time,and the range values of short time(ST)and long time(LT)are determined to satisfy the requirement of accuracy error within 5%.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
Backgrounds ATP is the major energy source for myotube contraction,and is quickly produced to compensate ATP consumption and to maintain sufficient ATP level.ATP is consumed mainly in cytoplasm and produced in mitocho...Backgrounds ATP is the major energy source for myotube contraction,and is quickly produced to compensate ATP consumption and to maintain sufficient ATP level.ATP is consumed mainly in cytoplasm and produced in mitochondria during myotube contraction.To understand the mechanism of ATP homeostasis during myotube contraction,it is essential to monitor mitochondrial ATP at single-cell level,and examine how ATP is produced and consumed in mitochondria.Methods:We established C2C12 cell line stably expressing fluorescent probe of mitochondrial ATP,and induced differentiation into myotubes・We gave electric pulse stimulation to the differentiated myotubes,and measured mitochondrial ATP.We constructed mathematical model of mitochondrial ATP at single-cell level,and analyzed kinetic parameters of ATP production and consumption.Results:We performed hierarchical clustering analysis of time course of mitochondrial ATP,which resulted in two clusters.Cluster 1 showed strong transient increase,whereas cluster 2 showed weak transient increase.Mathematical modeling at single-cell level revealed that the ATP production rate of cluster 1 was larger than that of cluster 2,and that both regulatory pathways of ATP production and consumption of cluster 1 were faster than those of cluster 2.Cluster 1 showed larger mitochondrial mass than cluster 2,suggesting that cluster 1 shows the similar property of slow muscle fibers,and cluster 2 shows the similar property of fast muscle fibers.Conclusions Cluster 1 showed the stronger mitochondrial ATP increase by larger ATP production rate,but not smaller consumption.Cluster 1 might reflect the larger oxidative capacity of slow muscle fiber.展开更多
文摘The increasing demand due to development and advancement in every field of life has caused the depletion of fossil fuels.This depleting fossil fuel reserve throughout the world has enforced to get energy from alternative/renewable sources.One of the economicalways to get energy is through the utilization of solar ponds.In this study,a mathematical model of a salt gradient solar pond under the Islamabad climatic conditions has been analyzed for the first time.The model uses a one-dimensional finite difference explicit method for optimization of different zone thicknesses.The model depicts that NCZ(Non-Convective Zone)thickness has a significant effect on LCZ(Lower Convective Zone)temperature and should be kept less than 1.7mfor the optimal temperature.It is also observed that for long-termoperation of a solar pond,heat should be extracted by keeping the mass flowrate of 17.3 kg/m^(2)/day.Themodel also suggests that when the bottom reflectivity is about 0.3,then only 24%of the radiation is absorbed in the pond.
基金Supported by National Key Basic Research Program of China(973 Program,Grant No.2014CB046405)Hebei Provincial Applied Basic Research Program(Grant No.12962147D)National Natural Science Foundation of China(Grant No.51375423)
文摘The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.
文摘We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.KFU252959].
文摘Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.
文摘In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to challenges,particularly concerning housing prices,which have drawn widespread societal attention.This article explores the theories of housing prices,analyzes factors influencing them,and conducts an empirical investigation of the impact of representative factors on ordinary residential prices.Using regression analysis and the entropy weight method,a mathematical model was developed to examine how various factors affect housing prices.
文摘Extensive historical data of a sewage treatment works are required by numerical models in order to simulate the biological processes accurately. However, the data are recorded mostly for daily operational purpose. They are basically not comprehensive enough to meet the modelling’s requirements. A comprehensive sampling protocol to accurately characterise the influent is required in order to determine all model components, which is very time-consuming and expensive. In a project of evaluating a sewage treatment works in Chongqing by using BioWin 4.1 for mathematical modelling, sensitivity analysis was conducted to determine the most critical parameters for process monitoring. It was found that influent characteristics, wasted sludge flow rate, water temperatures, DO levels of the biological tanks and five bio-kinetic parameters were the most influential parameters governing the plant performance. Therefore, apart from monitoring the effluent quality, regular checking of the afore-mentioned influential parameters can help examine the performance of a sewage treatment works. Moreover, operators of the sewage treatment works can conduct “what-if” analysis to determine how these most influential parameters can be adjusted to improve the treatment performance of the sewage treatment works.
文摘A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten kinetics. Analytical expression pertaining to the substrate concentration was reported for all possible values of Thiele module φ and α . In this work, we report the theoretically evaluated steady-state effectiveness factor for immobilized enzyme systems in porous spherical particles. These analytical results were found to be in good agreement with numerical results. Moreover, herein we employ new “Homotopy analysis method” (HAM) to solve non-linear reaction/diffusion equation.
基金supported by a grant from the Education Department of Zhejiang Province (No.Y200803235)
文摘Objective： The progression of human cancer is characterized by the accumulation of genetic instability. An increasing number of experimental genetic molecular techniques have been used to detect chromosome aberrations. Previous studies on chromosome abnormalities often focused on identifying the frequent loci of chromosome alterations, but rarely addressed the issue of interrelationship of chromosomal abnormalities. In the last few years, several mathematical models have been employed to construct models of carcinogenesis, in an attempt to identify the time order and cause-and-effect relationship of chromosome aberrations. The principles and applications of these models are reviewed and compared in this paper. Mathematical modeling of carcinogenesis can contribute to our understanding of the molecular genetics of tumor development, and identification of cancer related genes, thus leading to improved clinical practice of cancer.
文摘The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.
文摘In this paper,we developed a mathematical model for Streptococcus suis,which is an epidemic by considering the moisture that affects the infection.The disease is caused by Streptococcus suis infection found in pigs which can be transmitted to humans.The patients of Streptococcus suis were generally found in adults males and the elderly who contacted pigs or who ate uncooked pork.In human cases,the infection can cause a severe illness and death.This disease has an impact to the financial losses in the swine industry.In the development of models for this disease,we have divided the population into 7 related groups which are susceptible pig compartment,infected pig compartment,quarantined pig compartment,recovered pig compartment,susceptible human compartment,infected human compartment,and recovered human compartment.After that,we use this model and a quarantine strategy to analyze the spread of the infection.In addition,the basic reproduction number R0 is determined by using the next-generation matrix which can analyze the stability of the model.The numerical simulations of the proposed model are illustrated to confirm the results from theorems.The results showed that there is an effect from moisture to the disease transmission.When the moisture increases the disease infection also increases.
文摘Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories.Mathematicalmodels play an important role in the diagnosis and treatment of cancer.In this study,data of 42 BI-RADS 4 patients taken fromthe Center for Breast Health,Near East University Hospital is utilized.Regarding the analysis,a mathematical model is constructed by dividing the population into 4 compartments.Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk.Numerical simulations of the parameters are demonstrated.The results of the model have revealed that an increase in the lactation rate and earlymenopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age,the palpable mass,and family history is distinctive.Furthermore,the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined.Consequently,the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories.All things considered,with the assistance of the most effective parameters,the range of cancer risks in BI-RADS 4 subcategories will decrease.
文摘A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.
文摘Environmental conscious manufacturing has become an important issue in industry because of market pressure and environmental regulations. An environmental risk assessment model was developed based on the network analytic method and fuzzy set theory. The "interval analysis method" was applied to deal with the on site monitoring data as basic information for assessment. In addition, the fuzzy set theory was employed to allow uncertain, interactive and dynamic information to be effectively incorporated into the environmental risk assessment. This model is a simple, practical and effective tool for evaluating the environmental risk of manufacturing industry and for analyzing the relative impacts of emission wastes, which are hazardous to both human and ecosystem health. Furthermore, the model is considered useful for design engineers and decision maker to design and select processes when the costs, environmental impacts and performances of a product are taken into consideration.
文摘On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.
文摘Meningococcal meningitis(MCM)is one of the serious public health threats in the tropical and sub-tropical regions.In this paper,we propose an epidemic model to study the transmission dynamics of MCM with high-and low-risk susceptible populations.The model considers two different groups of susceptible individuals depending on the availability of medical resources(MR,including hospitals,health workers,etc.),which varies the infection risk.We find that the model exhibits the phenomenon of backward bifurcation(BB),which increases the difficulty of MCM control since the dynamics are not merely relying on the basic reproduction number,TZo.This study explores the effects of MR on the MCM epidemics by mathematical analysis and shows the existence of BB on MCM disease.Our findings suggest that providing adequate MR in a community is crucial in mitigating MCM incidences and deaths,especially,in the MCM endemic regions.
基金This project is supported by the National Science Foundation "Tian Yuan" Terms and LNM Institute of Mechanics Academy of ScienceThis project is supported by the NationalYunnan Province Natural Science Foundation of China
文摘In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are also considered.in particular,the conditions for the existence of Hopf bifurcation can be given in terms of the coefficients of the characteristic equation.The method extends the application of the Hopf bifurcation theorem to higher differential equations which occur in biological models,chemical models,and epidemiological models etc.
基金supported by the National Natural Science Foundation of China(51705242)Shanghai Sailing Program(16YF1404900)the Fundamental Research Funds for the Central Universities(NS2015072)
文摘Time-limited dispatching(TLD)analysis of the full authority digital engine control(FADEC)systems is an important part of the aircraft system safety analysis and a necessary task for the certification of commercial aircraft and aeroengines.In the time limited dispatch guidance document ARP5107B,a single-fault Markov model(MM)approach is proposed for TLD analysis.However,ARP5107B also requires that the loss of thrust control(LOTC)rate error calculated by applying the single-fault MM must be less than 5%when performing airworthiness certification.Firstly,the sources of accuracy errors in three kinds of MM are analyzed and specified through a case study of the general FADEC system,and secondly a two-fault MM considering maintenance policy is established through analyzing and calculating the expected repair time when two related faults happen.Finally,a specific FADEC system is given to study on the influence factors of accuracy error in the single-fault MM,and the results show that the accuracy error of the single-fault MM decreases with the increase of short or long prescribed dispatch time,and the range values of short time(ST)and long time(LT)are determined to satisfy the requirement of accuracy error within 5%.
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We thank laboratory members for critical reading of the manuscript and for technical assistance with the analysis.The computations for this work were performed in part on the NIG supercomputer system at ROIS National Institute of Genetics.This work was supported by the Creation of Fundamental Technologies for Understanding and Control of Biosystem Dynamics,CREST,of the Japan Science and Technology Agency(JST).S.K.was supported by the Japan Society for the Promotion of Science(JSPS)KAKENHI Grant Number(17H06300,17H6299,18H03979,19K22860)M.F.was supported by the Japan Society for the Promotion of Science(JSPS)KAKENHI Grant Number(16K1250&19K20382).
文摘Backgrounds ATP is the major energy source for myotube contraction,and is quickly produced to compensate ATP consumption and to maintain sufficient ATP level.ATP is consumed mainly in cytoplasm and produced in mitochondria during myotube contraction.To understand the mechanism of ATP homeostasis during myotube contraction,it is essential to monitor mitochondrial ATP at single-cell level,and examine how ATP is produced and consumed in mitochondria.Methods:We established C2C12 cell line stably expressing fluorescent probe of mitochondrial ATP,and induced differentiation into myotubes・We gave electric pulse stimulation to the differentiated myotubes,and measured mitochondrial ATP.We constructed mathematical model of mitochondrial ATP at single-cell level,and analyzed kinetic parameters of ATP production and consumption.Results:We performed hierarchical clustering analysis of time course of mitochondrial ATP,which resulted in two clusters.Cluster 1 showed strong transient increase,whereas cluster 2 showed weak transient increase.Mathematical modeling at single-cell level revealed that the ATP production rate of cluster 1 was larger than that of cluster 2,and that both regulatory pathways of ATP production and consumption of cluster 1 were faster than those of cluster 2.Cluster 1 showed larger mitochondrial mass than cluster 2,suggesting that cluster 1 shows the similar property of slow muscle fibers,and cluster 2 shows the similar property of fast muscle fibers.Conclusions Cluster 1 showed the stronger mitochondrial ATP increase by larger ATP production rate,but not smaller consumption.Cluster 1 might reflect the larger oxidative capacity of slow muscle fiber.
