mathematical model

摘要： Since the onset of the COVID-19 epidemic, the world has been impressed by two things: The number of people infected and the number of deaths. Here, we propose a mathematical model of the spread of this disease, analyze this model mathematically and determine one or more dominant factors in the propagation of the COVID-19 epidemic. We consider the S-E-I-R epidemic model in the form of ordinary differential equations, in a population structured in susceptibles S, exposed E as caregivers, travelers and assistants at public events, infected I and recovered R classes. Here we decompose the recovered class into two classes: The deaths class D and the class of those who are truly healed H. After the model construction, we have calculated the basic reproduction number R0, which is a function of certain number of parameters like the size of the exposed class E. In our paper, the mathematical analysis, which consists in searching the equilibrium points and studying their stability, is done. The work identifies some parameters on which one can act to control the spread of the disease. The numerical simulations are done and they illustrate our theoretical analysis.

摘要： The paper focuses on the prediction of the volumetric density property of knitting fabrics using mathematical modeling. Based on the graphical analysis of the obtained mathematical models, the results of the raw material properties for the futer knitted fabric on the values of alternative indicators are presented.

摘要： Our study is being carried out in the Wouri Estuary more precisely in the Nylon area, Douala. This area is influenced by abundant rainfall which promotes the phenomenon of rain erosion. This erosion contributes to the degradation of structures and soils. To better understand and predict this phenomenon of rainfall erosion, we set out to establish a mathematical model that takes into account precipitation and topography. To this end, the data collected in the field and in the laboratory made it possible. First, we graphically modeled the variation of the potential as a function of the intensity of rainfall and the slope of the ground. Next, we identified a mathematical model from cubic spline surface interpolation. Finally, we obtained the mathematical model which makes it possible to evaluate and predict the erosion potential. The results obtained allowed to have an erosion potential of 153.67 t/ha/year with field data and 153.94 t/ha/year with laboratory data. We compared the results obtained with those existing in the literature on the same study site. This comparison made it possible to validate the established mathematical model. This mathematical model is a decision support tool and can predict problems related to water, erosion and the environment.

摘要： The aim of this study is to examine the progress of the worldwide pandemic Covid-19.As authors,we have decided to analyze the situation of COVID-19 onMediterranean islandwith accurate data.For this purpose,amathematical model is constructed and proposed by dividing the whole population into sensible and suitable compartments.The study captures the dates February 01 till May 15,2021.For the control of the spread of disease,vaccination and infection rates are compared and calculated.During calculations and comparison,MatLab software is used.All of the data that are used are taken from the Ministry of Health.The effect of parameters is examined with sensitivity analysis.Furthermore,with this analysis,values of parameters are obtained.Afterwards,by using the constructed model,the effect of vaccine on infected individuals is analyzed separately.As a result,it is concluded that the studied part of the island is late for the control of the disease via vaccine.This can be explained by two main reasons;vaccinating the people that are not inmobilitymost of the time(aged people and people with chronic diseases)and getting the vaccine late.Hence,the results showed that this rate and distribution of vaccines would not be enough to control the pandemic on the island.

摘要： COVID-19 has become a pandemic,with cases all over the world,with widespread disruption in some countries,such as Italy,US,India,South Korea,and Japan.Early and reliable detection of COVID-19 is mandatory to control the spread of infection.Moreover,prediction of COVID-19 spread in near future is also crucial to better plan for the disease control.For this purpose,we proposed a robust framework for the analysis,prediction,and detection of COVID-19.We make reliable estimates on key pandemic parameters and make predictions on the point of inflection and possible washout time for various countries around the world.The estimates,analysis and predictions are based on the data gathered fromJohns Hopkins Center during the time span of April 21 to June 27,2020.We use the normal distribution for simple and quick predictions of the coronavirus pandemic model and estimate the parameters of Gaussian curves using the least square parameter curve fitting for several countries in different continents.The predictions rely on the possible outcomes of Gaussian time evolution with the central limit theorem of statistics the predictions to be well justified.The parameters of Gaussian distribution,i.e.,maximumtime and width,are determined through a statisticalχ^(2)-fit for the purpose of doubling times after April 21,2020.For COVID-19 detection,we proposed a novel method based on the Histogram of Oriented Gradients(HOG)and CNN in multi-class classification scenario i.e.,Normal,COVID-19,viral pneumonia etc.Experimental results show the effectiveness of our framework for reliable prediction and detection of COVID-19.

摘要： Diabetes disorder turns smoothly to be a global epidemic disorder and the glycated hemoglobin(HbA1c)starts to be an efficient marker of it.The dielectric spectroscopy on different human normal-and diabetic-blood samples is used to characterize and to estimate the HbA1c concentration.“dc-”and ac-measurement of the complex conductivity in the temperature range from 280 K up to 320 K,and in the frequency range from one Hz up to 32 MHz have been performed.The thermal activation energy,ΔEσ,of dc-electric conductivity lies in the range 95 meV<ΔEσ<115 meV;while the thermal activation energy,ΔEτ,of RBCs relaxation time is aboutΔEτ=140 meV.The experimental data have been modeled by a physical-model and good fittings have been found between calculated and experimental values.The effective number of charges,nG,T,is estimated after Cole and Cole curves.One has found that nG,T increases with both temperature,T,and with the glycation rate GG.This increase may shed some light on an effective and possible way to treat(and to detect)diabetes disorders via eliminating the excess electric charges produced by glycation processes.The present work sheds the light on the possible combination of focused ultrasound with magnetic resonance imaging to study the dielectric-thermal variations of glycated-RBCs,which can lead to very precise and non-invasive monitoring of glycation concentration in vivo and in vitro via magnetic resonance-thermometry.

摘要： 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.

摘要： 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.

摘要： In order to enhance the production of biogas and to study the thermal behavior of waste, a numerical study of fluid flows and heat transfers within household waste was developed to predict the distributions of thermal fields. The mathematical model is based on the conservation of mass and energy equations. The resulting system of equations is discretized using the finite volume method and solved using the Thomas algorithm. The results of the model studied are compared with the numerical and site measurements results from other authors. The results have been found to be in good agreement. The results show that the mathematical model is able to reproduce the thermal behavior in anaerobic phase in landfills. The isotherms revealed that temperatures are lower in the upper part of the waste cell, very high in the core and decrease slightly in the bottom of the cell due to the biodegradation of waste.

摘要： Residential photovoltaic (PV) systems connected to the grid are used for self-consumption. Any surplus production is fed into the grid and contributes to improving the voltage. Several techniques are developed to model their connection. However, studies on methods of injecting energy production into the Low Voltage (LV) network are nowadays a problem. This paper proposes a mathematical model to determine the current to be injected and calculate each node’s voltage. The current equation is a recurrence relation with an initial condition. This initial condition is for the case of a single PV system connected to the LV grid. The equation can also be written in matrix form. Similarly, the voltage solution is a recurrence relation. It also has an initial condition for the first node. Both mathematical formulae with the proposed initial conditions are consistent and can be used for the determination of the current and voltage of the different nodes in the grid.

摘要： The level of packing automation increase rapidly. To realize different complex packing，using the robot system to simulate the movement of human hands is just needed. This paper using trajectory planning based on spline function，rigid robot Lagrangian kinetics set up system mathematical model. This method offers a new thought way for designing automation packing rigid robot system.

摘要： The level of packing automation increase rapidly. To realize different complex packing，using the robot system to simulate the movement of human hands is just needed. This paper using trajectory planning based on spline function，rigid robot Lagrangian kinetics set up system mathematical model. This method offers a new thought way for designing automation packing rigid robot system.

摘要： The level of packing automation increase rapidly. To realize different complex packing，using the robot system to simulate the movement of human hands is just needed. This paper using trajectory planning based on spline function，rigid robot Lagrangian kinetics set up system mathematical model. This method offers a new thought way for designing automation packing rigid robot system.

摘要： The level of packing automation increase rapidly. To realize different complex packing，using the robot system to simulate the movement of human hands is just needed. This paper using trajectory planning based on spline function，rigid robot Lagrangian kinetics set up system mathematical model. This method offers a new thought way for designing automation packing rigid robot system.