scholarly journals Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach

2020 ◽  
Vol 25 (3) ◽  
pp. 42
Author(s):  
Yasushi Ota ◽  
Naoki Mizutani
Keyword(s):  
Mathematical Model ◽  
Bayesian Inference ◽  
Diffusion Of Innovation ◽  
Model Fitting ◽  
Sir Model ◽  
Actual Data ◽  
Diffusion Of Innovation Theory ◽  
Mathematical Properties ◽  
Proposed Model ◽  
The Stability

In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute oscillations of actual data by means of our proposed model.

scholarly journals Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach

2019 ◽  
Author(s):  
Yasushi Ota ◽  
Naoki Mizutani
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Bayesian Inference ◽  
Model Fitting ◽  
Actual Data ◽  
Mathematical Properties ◽  
Proposed Model ◽  
The Stability

In this study, based on our previous study, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient booms and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute vibrations of actual data by means of our proposed model.

scholarly journals Mathematical Regression Models for Analyzing and Forecasting Diabetes prevalence in Oman

2021 ◽  
Author(s):  
Jabar Yousif
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Regression Models ◽  
Diabetes Type 2 ◽  
Diabetes Type ◽  
Actual Data ◽  
Sultanate Of Oman ◽  
Proposed Model ◽  
Future Data

<p>This work is concerned with proposing mathematical models characterized by accuracy and ease in predicting the number of diabetics type 2 in the Sultanate of Oman. By analyzing the proposed mathematical models of the current work (1, 2, and 3), it was found that the proposed mathematical model in Equation 6 can accurately predict the number of diabetics in Oman up to 2050. In order to test the model's accuracy and validity, we revised it with actual data. The results prove the accuracy of the proposed model in predicting future data of 99%. Lastly, several recommendations were recorded that could help to reduce the prevalence of diabetes type 2 in Oman.</p>

scholarly journals On Mathematical Modelling of the Indian Human Hair Industry in the Post-COVID-19 Era

2021 ◽  
Vol 8 (3) ◽  
pp. 447-452
Author(s):  
Shibam Manna ◽  
Tanmay Chowdhury ◽  
Asoke Kumar Dhar ◽  
Juan Jose Nieto
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Human Hair ◽  
Control Parameter ◽  
Employment Opportunities ◽  
Alternative Employment ◽  
Job Opportunities ◽  
Proposed Model ◽  
The Stability ◽  
The Impact

An attempt to model the human hair industry in the post-COVID-19 pandemic situation using mathematical modelling has been the goal of this article. Here we introduce a novel mathematical modelling using a system of ordinary differential equations to model the human hair industry as well as the human hair waste management and related job opportunities. The growth of human hair in the months of nationwide total lockdown has been taken into account and graphs have been plotted to analyze the effect of Lockdown in this model. The alternative employment opportunities that can be created for collecting excessive hair in the post-pandemic period has been discussed. A probable useful mathematical model and mechanism to utilize the migrant labours who became jobless due to the pandemic situation and the corresponding inevitable lockdown situation resulting out of that crisis has been discussed in this paper. We discussed the stability analysis of the proposed model and obtained the criteria for an optimal profit of the said model. Graphs have also been plotted to analyze the impact of the control parameter on the optimal profit.

Role of technology in combating social crimes: A modeling study

2013 ◽  
Vol 24 (4) ◽  
pp. 501-514 ◽  
Author(s):  
J. B. SHUKLA ◽  
ASHISH GOYAL ◽  
KAPIL AGRAWAL ◽  
HARSH KUSHWAH ◽  
AJAY SHUKLA
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Susceptible Population ◽  
Use Of Technology ◽  
Proposed Model ◽  
Intensive Use ◽  
Immigration And Emigration ◽  
The Stability ◽  
Dynamic Population

In this paper, a non-linear mathematical model is proposed and analysed to study the role of technology in combating social crimes in a dynamic population by considering immigration and emigration rates of susceptible population and criminals. The problem is modelled by considering five interacting variables, namely the density of susceptible population, the density of criminals, the density of removed (isolated) criminals, the density of crime burden and the level of technology used to control crime. The proposed model is analysed by using the stability theory of differential equation and simulation. The model analysis shows that the crime burden decreases considerably as the level of technology increases. It is noted that the crime in a society can be controlled almost completely if criminals from the general population are removed by intensive use of technology.

scholarly journals Mathematical Regression Models for Analyzing and Forecasting Diabetes prevalence in Oman

2021 ◽  
Author(s):  
Jabar Yousif
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Regression Models ◽  
Diabetes Type 2 ◽  
Diabetes Type ◽  
Actual Data ◽  
Sultanate Of Oman ◽  
Proposed Model ◽  
Future Data

<p>This work is concerned with proposing mathematical models characterized by accuracy and ease in predicting the number of diabetics type 2 in the Sultanate of Oman. By analyzing the proposed mathematical models of the current work (1, 2, and 3), it was found that the proposed mathematical model in Equation 6 can accurately predict the number of diabetics in Oman up to 2050. In order to test the model's accuracy and validity, we revised it with actual data. The results prove the accuracy of the proposed model in predicting future data of 99%. Lastly, several recommendations were recorded that could help to reduce the prevalence of diabetes type 2 in Oman.</p>

scholarly journals A mathematical Model for the Dynamics of COVID-19 Pandemy Involving the Infective Immigrants

2021 ◽  
pp. 295-307
Author(s):  
Ahmed A. Mohsen ◽  
Hassan F. AL-Husseiny ◽  
Khalid Hattaf ◽  
Bilal Boulfoul
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Foreign Students ◽  
Dynamical Behavior ◽  
Foreign Workers ◽  
Proposed Model ◽  
Rapid Spread ◽  
The Stability ◽  
Control And Management ◽  
Stability Results

Since the first outbreak in Wuhan, China, in December 31, 2019, COVID-19    pandemy  ‎has been spreading to many countries in the world. The ongoing COVID-19 pandemy has caused a ‎major global crisis, with 554,767 total confirmed cases, 484,570 total recovered cases, and ‎‎12,306 deaths in Iraq as of February 2, 2020. In the absence of any effective therapeutics or drugs ‎and with an unknown epidemiological life cycle, predictive mathematical models can aid in ‎the understanding of both control and management of coronavirus disease. Among the important ‎factors that helped the rapid spread of the epidemy are immigration, travelers, foreign workers, and foreign students. In this work, we develop a mathematical model to study the dynamical ‎behavior of COVID-19 pandemy, involving immigrants' effects with the possibility of re-infection. ‎Firstly, we studied the positivity and roundedness of the solution of the proposed model. The stability ‎results of the model at the disease-free equilibrium point were presented when . Further, it was proven that the pandemic equilibrium point will persist uniformly when . Moreover, we ‎confirmed the occurrence of the local bifurcation (saddle-node, pitchfork, and transcritical). Finally, ‎theoretical analysis and numerical results were shown to be consistent.

scholarly journals Susceptible-Infected-Removed Mathematical Model under Deep Learning in Hospital Infection Control of Novel Coronavirus Pneumonia

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ting Liu ◽  
Yanling Bai ◽  
Mingmei Du ◽  
Yueming Gao ◽  
Yunxi Liu
Keyword(s):  
Mathematical Model ◽  
Deep Learning ◽  
Infection Control ◽  
Model Fitting ◽  
Sir Model ◽  
Hospital Infection ◽  
Model Based ◽  
Hospital Infection Control ◽  
Stochastic Sir ◽  
Novel Coronavirus

Objective. This research aimed to explore the application of a mathematical model based on deep learning in hospital infection control of novel coronavirus (COVID-19) pneumonia. Methods. First, the epidemic data of Beijing, China, were utilized to make a definite susceptible-infected-removed (SIR) model fitting to determine the estimated value of the COVID-19 removal intensity β, which was then used to do a determined SIR model and a stochastic SIR model fitting for the hospital. In addition, the reasonable β and γ estimates of the hospital were determined, and the spread of the epidemic in hospital was simulated, to discuss the impact of basal reproductive number changes, isolation, vaccination, and so forth on COVID-19. Results. There was a certain gap between the fitting of SIR to the remover and the actual data. The fitting of the number of infections was accurate. The growth rate of the number of infections decreased after measures, such as isolation, were taken. The effect of herd immunity was achieved after the overall immunity reached 70.9%. Conclusion. The SIR model based on deep learning and the stochastic SIR fitting model were accurate in judging the development trend of the epidemic, which can provide basis and reference for hospital epidemic infection control.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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