Mathematical model for smoking: Effect of determination and education

2015 ◽  
Vol 08 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Anuradha Yadav ◽  
Prashant K. Srivastava ◽  
Anuj Kumar
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Mathematical Models ◽  
Smoking Behavior ◽  
Threshold Value ◽  
Educational Programs ◽  
Feasible Region ◽  
Quit Smoking ◽  
Positivity And Boundedness

We propose and analyze mathematical models to study the dynamics of smoking behavior under the influence of educational programs and also individual's determination to quit smoking. We establish the positivity and boundedness of the solutions in a biologically feasible region. A threshold value responsible for persistence of smoking is obtained and stability analysis on models is performed. We find that determination alone is not enough to eradicate smoking but it can reduce the prevalence of smoker population. Whereas the increase in education can possibly eradicate it. We performed numerical simulation for representative set of parameters to verify and discuss results obtained analytically.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

Modeling and Stability Analysis of Hydraulic System for Wave Simulation

2013 ◽  
Vol 291-294 ◽  
pp. 1934-1939
Author(s):  
Jian Jun Peng ◽  
Yan Jun Liu ◽  
Yu Li ◽  
Ji Bin Liu
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Mathematical Models ◽  
Hydraulic System ◽  
Simulation System ◽  
Displacement Sensor ◽  
Schematic Diagram ◽  
Wave Simulation ◽  
The Stability ◽  
The Mathematical Model

This thesis put forward a hydraulic wave simulation system based on valve-controlled cylinder hydraulic system, which simulated wave movement on the land. The mathematical model of valve-controlled symmetric cylinder was deduced and the mathematical models of servo valve, displacement sensor and servo amplifier were established according to the schematic diagram of the hydraulic system designed, on the basis of which the mathematical model of hydraulic wave simulation system was obtained. Then the stability of the system was analyzed. The results indicated that the system was reliable.

scholarly journals DYNAMICS OF ENVIRONMENTAL POLLUTIONTHROUGH VEHICLES

2020 ◽  
Vol 5 (4) ◽  
pp. 38-47
Author(s):  
Nita Shah ◽  
Shreya Patel ◽  
Moksha Satia ◽  
Foram Thakkar
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Air Pollution ◽  
Stability Analysis ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
System Stability ◽  
System Stability Analysis ◽  
Almost All ◽  
Day By Day

In today’s time as air pollution is increasing day by day the use of non-polluted has to be increased in almost all nooks and corner of the countries. In this paper a mathematical model is developed to analyse environmental pollution through polluted and non-polluted vehicles. Basic reproduction number has been calculated which will the decide the behavior of the system. Stability analysis has been carried out at equilibrium points. Numerical simulation is done to analyse the result for various compartments.

scholarly journals Mathematical Assessment of the Dynamical Model of Smoking Tobacco Epidemic in Bangladesh

2020 ◽  
pp. 36-48
Author(s):  
Sk. Abdus Samad ◽  
Md. Tusberul Islam ◽  
Sayed Toufiq Hossain Tomal ◽  
MHA Biswas
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Differential Equations ◽  
Basic Reproduction Number ◽  
Conversion Rate ◽  
Reproduction Number ◽  
The World ◽  
Tobacco Epidemic ◽  
The Basic Reproduction Number

Bangladesh is one of the largest tobacco users in the world being troubled by smoking related issues. In this paper we consider a compartmental mathematical model of smoking in which the population is divided into five compartments: susceptible, expose, smokers, temporary quitters and permanent quitters described by ordinary differential equations. We study by including the conversion rate from light smoker to permanent quit smokers. The basic reproduction number R0 has been derived and then we found two euilibria of the model one of them is smoking-free and other of them is smoking-present. We establish the positivity, boundedness of the solutions and perform stability analysis of the model. To decrease the smoking propensity in Bangladesh we perform numerical simulation for various estimations of parameters which offer understanding to give up smoking and how they influence the smoker and exposed class. This model gives us legitimate thought regarding the explanations for the spread of smoking in Bangladesh.

scholarly journals Stability Analysis of Mathematical Model of a Relapse Tuberculosis Incorporating Vaccination

2021 ◽  
Vol 7 (1) ◽  
pp. 116-130
Author(s):  
O. Odetunde ◽  
◽  
M.O. Ibrahim ◽  
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Medical Attention ◽  
Infectious Individual ◽  
Specific Data ◽  
Proposed Model ◽  
Tuberculosis Disease

A general SIQRM epidemic model with vaccination and relapse possibility is proposed for analysis in this work. The idea behind the proposed model is to check the effect of immunity obtained from vaccine or treatment, quarantine effect as well as waning effect of immunity on the transmission rate of Tuberculosis within a population that is subjected to proper education without restricted access. Some other infectious diseases in this category include measles and Ebola. Two equilibrium states of the proposed model are obtained as well as the effective reproduction number(Reff). Stability analysis of the model at the Infection Free Equilibrium(I.F.E) state is established on the condition that Reff<1. Numerical simulation for the general SIQRM model was done using specific data for Tuberculosis disease and the result shows that proper education, vaccination and early diagnosis of an infectious individual for quarantining is an efficient way by which the spread of Tuberculosis can be reduced in the population while adequate medical attention yield better result for detected cases

scholarly journals Stability analysis of a mathematical model for awareness initiatives on registration of persons in Kenya

2020 ◽  
Vol 9 (1) ◽  
pp. 21
Author(s):  
ANN N. Mwambia ◽  
Mark O. Okongo ◽  
Gladys G. Njoroge
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Word Of Mouth ◽  
Reproduction Number ◽  
Electronic Media ◽  
Asymptotically Stable ◽  
Boundedness Of Solutions ◽  
Globally Asymptotically Stable ◽  
Next Generation Matrix ◽  
Positivity And Boundedness

In this paper, we discuss stability analysis of a mathematical model of awareness initiatives in registration of persons in Kenya. Using Ordinary Differential Equations, a mathematical model to compare the efficacy of print media, electronic media and word-of-mouth media in disseminating registration information is developed. Positivity and boundedness of solutions is established to ensure that the model is mathematically meaningful. The Basic Reproduction number R0 is derived using the Next Generation Matrix. We present both awareness free equilibrium and the maximum awareness equilibrium. Stability analysis of the model shows that Awareness free equilibrium is both locally and globally asymptotically stable when R0 < 1 hence no spread of awareness and unstable when R0 > 1 while MAE is locally asymptotically stable when R0 > 1 indicating spread of information in the population.  

scholarly journals Stability analysis of a smoking behavior model

2021 ◽  
Vol 2106 (1) ◽  
pp. 012025
Author(s):  
S M Lestari ◽  
Y Yulida ◽  
A S Lestia ◽  
M A Karim
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Smoking Behavior ◽  
Asymptotically Stable ◽  
Runge Kutta Method ◽  
The Stability ◽  
The Basic Reproduction Number

Abstract This research discussed the mathematical model of smoking behavior. The model will be analogous to an epidemic model which will be divided into several compartments/groups. This research aimed to explain the formation of a mathematical model of smoking behavior, to investigate the equilibrium point, the value of the basic reproduction number, to analyze the stability of the model, then to determine and interpret the numerical solutions using the fourth-order Runge-Kutta method. By the results of this research, a mathematical model of smoking behavior which consists of three compartments, namely the population of non-smokers, smokers and ex-smokers, was obtained. Based on the model formed the smoke-free equilibrium point and the smoker equilibrium point, then the basic reproduction number was also obtained using the next generation matrix. Furthermore, the result of the stability analysis of the smoker-free population was asymptotically stable provided that the basic reproduction number is less than one, while the population was asymptotically stable provided that the basic reproduction number is greater than one. The simulation of the model was presented to support the explanation of the stability analysis of the model using the fourth-order Runge-Kutta method based on the parameters that met the requirements of the stability analysis.

scholarly journals Comparison of 2D and 3D Models of Salinity Numerical Simulation

2015 ◽  
Vol 22 (s1) ◽  
pp. 26-29
Author(s):  
Li Chunhui ◽  
Pan Xishan ◽  
Ke Jie ◽  
Dong Xiaotian
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
3D Models ◽  
Seawater Desalination ◽  
Salinity Distribution ◽  
Before And After ◽  
Hydrodynamic Environment ◽  
2D And 3D ◽  
Important Significance

Abstract For the study of the effect of 2D and 3D mathematical model in salinity simulation, with Liuheng island strong brine discharge of seawater desalination project as an example, using 2D and 3D salinity mathematical models of Liuheng island to simulate coastal hydrodynamic environment and salinity distribution before and after the concentrated brine discharge, and analyzed the results. Finally got the applicable scope of the two models, it has an important significance in the study of similar problems.

A mathematical model and an algorithm for sampling sets of components on the Assembly enterprises of space technology

2018 ◽  
Vol 15 (1) ◽  
pp. 39-55
Author(s):  
V. B. Rudakov ◽  
V. M. Makarov ◽  
M. I. Makarov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Space Technology ◽  
Economic Costs ◽  
Problem Statement ◽  
Optimal Plan ◽  
Product Mix ◽  
Technical Parameters ◽  
Complex Products ◽  
Assembly Plants

The article considers the problem of determining the rational plans of the input sampling reliability and technical parameters of components of space technology, the totality of which is supplied to the Assembly plants for the manufacture of complex products of space technology. Problem statement and mathematical model based on the minimization of the economic costs of control and losses related to the risks of taking wrong decisions, are given in the article. The properties of the mathematical models are investigated, the algorithm for its optimization is developed. The result is an optimal plan for the sampling of sets of components, which includes: an optimal product mix subject to mandatory control of the aggregate and optimum risks of first and second kind, when acceptance number of statistical plan is zero. The latter circumstance is due to the high requirements of reliability and technical parameters of products of space technology.

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