Dynamic Analysis of the Effect of Quitting Smoking Applications on Smoking Cessation

2020 ◽  
pp. 74-94
Author(s):  
A. George Maria Selvam ◽  
Mary Jacintha
Keyword(s):  
Time Series ◽  
Smoking Cessation ◽  
Linear System ◽  
Dynamic Analysis ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
System Of Differential Equations ◽  
Bifurcation Diagrams ◽  
Quitting Smoking ◽  
Non Linear System

In this chapter, the authors considered a smoking cessation model formulated with a non-linear system of differential equations and obtained the continuous fractional order model and through discretization its discrete form to study the effectiveness of quitting smoking applications in giving up smoking. The existence of smoking free equilibria and smoking present equilibria are discussed, and the dynamical analysis of these two equilibria is put forward with the assistance of the smoking generation number. The numerical simulations aided by time series, phase portraits, and bifurcation diagrams confirm the results that are obtained analytically.

scholarly journals Analysis of Dynamical Behavior for Epidemic Disease COVID-19 with Application

2021 ◽  
Vol 12 (4) ◽  
pp. 568-577
Author(s):  
Dr. Maysoon M. Aziz, Et. al.
Keyword(s):  
Time Series ◽  
Linear System ◽  
Power Spectrum ◽  
Dynamical Behavior ◽  
Simulated Data ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Disease ◽  
The World ◽  
Non Linear System

In this paper, we will use the differential equations of the SIR model as a non-linear system, by using the Runge-Kutta numerical method to calculate simulated values for known epidemiological diseases related to the time series including the epidemic disease COVID-19, to obtain hypothetical results and compare them with the dailyreal statisticals of the disease for counties of the world and to know the behavior of this disease through mathematical applications, in terms of stability as well as chaos in many applied methods. The simulated data was obtained by using Matlab programms, and compared between real data and simulated datd were well compatible and with a degree of closeness. we took the data for Italy as an application.  The results shows that this disease is unstable, dissipative and chaotic, and the Kcorr of it equal (0.9621), ,also the power spectrum system was used as an indicator to clarify the chaos of the disease, these proves that it is a spread,outbreaks,chaotic and epidemic disease .

One Method for Restoring Inhomogeneous Attractors

1998 ◽  
Vol 08 (04) ◽  
pp. 825-833 ◽  
Author(s):  
Natalia B. Janson ◽  
Alexey N. Pavlov ◽  
Vadim S. Anishchenko
Keyword(s):  
Time Series ◽  
Simple Form ◽  
The Other ◽  
Phase Portraits ◽  
System Of Differential Equations ◽  
Global Modeling ◽  
Simple Shape ◽  
Biological Origin ◽  
Qualitative Models ◽  
Global Reconstruction

Several methods of restoration of phase portraits were applied to real experimental realizations a(t) of biological origin. The algorithms for global reconstruction were used to create qualitative models of the regimes under study. The results of global modeling were satisfactory for the time series of simple shape, but in case of complicated inhomogeneous realizations the traditional algorithms did not give reasonable models. We suggest a method for restoration of inhomogeneous attractors on a(t) as follows: [Formula: see text] while the other coordinates could be restored by any known methods (delay, differentiation, etc.). Such a representation of the attractor's coordinates preserves a simple form of the first equation of the system of differential equations sought [Formula: see text] This method was tested first on an artificially produced inhomogeneous realization containing pieces with very slow and very quick motion. After that it was successfully applied to real biological inhomogeneous realizations.

scholarly journals Seasonal variation and change trends for quit smoking: evidence from Internet search engine query data

2020 ◽  
Author(s):  
Dingtao Hu ◽  
Xiaoqi Lou ◽  
Nana Meng ◽  
Qiaomei Xie ◽  
Man Zhang ◽  
...  
Keyword(s):  
Time Series ◽  
Smoking Cessation ◽  
Seasonal Variation ◽  
New Zealand ◽  
Google Trends ◽  
Quit Smoking ◽  
Significant Seasonal Variation ◽  
Quitting Smoking ◽  
The Usa ◽  
The Uk

Abstract Background: The outcomes of smoking have generated considerable clinical interest in recent years. Although people from different countries are more interested in the topic of quit smoking during the winter, few studies have tested this hypothesis. The current study aimed to quantify public interest in quitting smoking via Google.Methods: We use Google Trends to obtain the Internet search query volume for terms relating to quit smoking in major northern and southern hemisphere countries in this research. Normally search volumes for the term “quit smoking + stop smoking + smoking-cessation” were retrieved within the USA, the UK, Canada, Ireland, New Zealand and Australia from January 2004 to December 2018. Seasonal effects were investigated using cosinor analysis and seasonal decomposition of time series models.Results: Significant seasonal variation patterns in those search terms were revealed by cosinor analysis and demonstrated by the evidence from Google Trends analysis in the representative countries including the USA (pcos = 2.36×10-7), the UK (pcos < 2.00×10-16), Canada (pcos < 2.00×10-16), Ireland (pcos <2.00×10-16) ,Australia (pcos = 5.13×10-6) and New Zealand (pcos = 4.87×10-7). Time series plots emphasized the consistency of seasonal trends with peaks in winter / late autumn by repeating in nearly all years. The overall trend of search volumes for quitting smoking, observed by dynamic series analysis, has declined from 2004 to 2018.Conclusions: The preliminary evidence from Google Trends search tool showed a significant seasonal variation and a decreasing trend for the RSV of quit smoking. Our novel findings in smoking-cessation epidemiology need to be verified with further studies, and the mechanisms underlying these findings must be clarified.

scholarly journals Dynamics and Stability of Hopf Bifurcation for One Non-linear System

TEM Journal ◽  
2021 ◽  
pp. 820-824
Author(s):  
Vahidin Hadžiabdić ◽  
Midhat Mehuljić ◽  
Jasmin Bektešević ◽  
Adnan Mašić
Keyword(s):  
Hopf Bifurcation ◽  
Linear System ◽  
Differential Equations ◽  
Detailed Analysis ◽  
Limit Cycle ◽  
Local Stability ◽  
System Of Differential Equations ◽  
The One ◽  
Non Linear System ◽  
The Given

In this paper we will look at the one system of ODE and analyze it. We aim to determine the points of equilibrium; examine their character and establish the existence of a bifurcation for the corresponding parameter value. A detailed analysis of local stability was performed for all values of the given parameter. For a certain value of the parameter, the existence of supercritical Hopf bifurcation of the observed system of differential equations has been proved. Also, the existence of a limit cycle that is always stable has been proved.

scholarly journals Bilateral approximations and periodic solutions of systems of differential equations with impulses

1985 ◽  
Vol 31 (2) ◽  
pp. 293-307
Author(s):  
S.G. Hristova ◽  
D.D. Bainov
Keyword(s):  
Periodic Solution ◽  
Linear System ◽  
Differential Equations ◽  
Periodic Solutions ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Non Linear ◽  
Impulsive Perturbations ◽  
Non Linear System

The paper justifies a method of bilateral approximations for finding the periodic solution of a non-linear system of differential equations with impulsive perturbations at fixed moments of time.

scholarly journals Analytical solution of system of differential equations by variational iteration method

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 77-86
Author(s):  
Jamshad Ahmed ◽  
Faizan Hussain
Keyword(s):  
Linear System ◽  
Analytical Solution ◽  
Differential Equations ◽  
Iteration Method ◽  
Graphical Representation ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Numerical Results ◽  
System Of Differential Equations ◽  
Non Linear System

In this paper, Varitational Iteration Method using He’s Polynomials is used to construct the exact as well as approximate solutions of differential equations. From the obtained numerical results, it has been observed that this proposed technique is very efficient and reliable for the solution of the linear and non-linear system of differential equations. Numerical results and graphical representation reflect the accuracy and effectiveness of the proposed modification.BIBECHANA 13 (2016) 77-86

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