Analysing Social Epidemics by Delayed Stochastic Models

Alcohol consumption in Spain has traditionally followed the Mediterranean drinking pattern, featuring daily drinking with meals, beer as the preferred beverage, and comparatively little drinking to intoxication. Alcohol dependence (AD), one of the most detrimental disorders caused by alcohol, was prevalent in 0.2% of women and 1.2% of men, corresponding to 31,200 women and 186,000 men in Spain with AD in 2005 in the age group of 15 to 64 year. These prevalence estimates of alcohol dependence are likely underestimated due to limitations in the World Mental Health Survey which cannot be fully corrected for; however, the estimates of AD for Spain represent the most accurate and up to date estimates available. Alcohol creates a significant health burden in Spain with 11.3 premature deaths in women per 100,000 aged 15 to 64 years, and 40.9 premature deaths in men per 100,000 in the same age group were due to alcohol consumption (data for 2004). This amounts to 8.4% of all female deaths and 12.3% of all the male deaths in this age group being attributable to alcohol consumption. A large percentage of these harms were due to heavy alcohol consumption and AD. AD is undertreated in Spain, with less than 10% of all people with AD treated. For those who are treated, psychotherapy is the most utilized form of treatment to avoid relapse. If 40% of AD patients in Spain were treated with pharmacological treatment (the most effective treatment method), 2.2% of female and 6.2% of male deaths due to AD would be prevented within one year. Thus by increasing treatment rates is an important means of reducing the alcohol-attributable mortality and health burden in Spain.

This paper is a comprehensive review of the available information about alcohol consumption in Spain. Alcohol use is the most severe drug problem among both young people and adults; almost half the Spanish population drink daily, and more than a fourth drink a quantity of alcohol sufficient to cause health problems in the long term. The consumption of alcohol may be considered to be culturally rooted when compared with other drug use which follows a more recent epidemic pattern. For those who use other drugs, for example cannabis and cocaine, alcohol is commonly used in conjunction. Clearly the level of alcohol use and abuse is high in Spain and constitutes a severe public health and socioeconomic problem.

A study on the conformable model of alcohol consumption in Spain has been presented. For the proposed model, the existence as well as the uniqueness of the solution has been discussed with the help of fixed-point theory. An analytical technique, Variational Iteration Method (VIM), has been used to obtain the solution to the governing system of differential equations. With the help of suitable plots, the role of fractional order derivative has been highlighted. For decreasing values of fractional order derivative, decrease in the number of non-consumers and non-risk consumers has been observed. By increasing the value of fractional order derivative, a sharp decrease can be seen in the compartment of risk-consumers. The agreement between the current study and the already existing studies, with ordinary derivatives, has also been pointed out.

Evolution of the prevalence of alcohol consumption and characterization of hazardous consumption in Spain: 2005-2022

Alcohol consumption in Mediterranean countries is in a transition period. The objective is to describe in the Spanish adult population the pattern of alcohol consumption by major sociodemographic variables. A cross-sectional study among 20,608 individuals aged ≥ 15 years who participated in the Spanish Health Interview Survey (ENS) 2011-2012. According to average intake, people were classified as heavy drinkers if they drank ≥ 40 g/day of alcohol (men) or ≥ 24 g/day (women). Binge drinking was defined as the consumption of ≥ 6 standard drinks (men) and ≥ 5 (women) at any drinking occasion (4-6 hours) in the last year. The beverage preference and the trend for 1987-2012 (ENS of these years) were estimated. The relationship of the distribution of drinking patterns with sociodemographic variables was analyzed using adjusted logistic regression models. The prevalence of heavy drinkers was 1.3% (2% in men and 0.7% in women). In men, heavy drinking was more frequent among 45 to 64 year olds (odds ratio (OR)=2.92 compared to men of 15-29 years; CI 95%: 1.59-5.38) and those born in Spain (OR=3.45; CI 95%: 1.59-7.69). In women, the only differences observed were those regarding education level, with heavy drinking increasing as the level of education increases (p linear trend <0.001). The prevalence of binge drinking during the last year was 19.6% in men and 7.1% in women. In both genders, the risk of binge drinking decreased with age and increased with higher education level (p linear trend <0.001). The standardized prevalence of heavy drinkers has declined from 18.8% in 1987 to 1.3% in 2012. Alcohol consumption in Spain is consistent with the model for countries in transition, where binge drinking is the most common pattern of excessive use of alcohol. A strong decline in heavy drinkers was observed and wine has been displaced by beer in beverage preference.

Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into the asymptotic stability of such cycles. In particular, we found a sufficient condition for asymptotic stability, and we gave algebraic criteria for deciding when this condition is also necessary. These criteria are satisfied for cycles in R3.Field and Swift, and Hofbauer, considered examples in R4 for which our sufficient condition for stability is not optimal. They obtained necessary and sufficient conditions for asymptotic stability using a transition-matrix technique.In this paper, we combine our previous methods with the transition-matrix technique and obtain necessary and sufficient conditions for asymptotic stability for a larger class of heteroclinic cycles. In particular, we obtain a complete theory for ‘simple’ heteroclinic cycles in R4 (thereby proving and extending results for homoclinic cycles that were stated without proof by Chossat, Krupa, Melbourne and Scheel). A partial classification of simple heteroclinic cycles in R4 is also given. Finally, our stability results generalize naturally to higher dimensions and many of the higher-dimensional examples in the literature are covered by this theory.

The known mathematical model of rumor spreading, which is described by a system of four nonlinear differential equations and is very popular in research, is considered. It is supposed that the considered model is influenced by stochastic perturbations that are of the type of white noise and are proportional to the deviation of the system state from its equilibrium point. Sufficient conditions of stability in probability for each from the five equilibria of the considered model are obtained by virtue of the Routh–Hurwitz criterion and the method of linear matrix inequalities (LMIs). The obtained results are illustrated by numerical analysis of appropriate LMIs and numerical simulations of solutions of the considered system of stochastic differential equations. The research method can also be used in other applications for similar nonlinear models with the order of nonlinearity higher than one.

Summary The nonlinear delay differential equation with exponential and quadratic nonlinearities is considered. It is assumed that the equation is exposed to stochastic perturbations of the white noise type, which are directly proportional to the deviation of the system state from the equilibrium point. Sufficient conditions for stability in probability of the zero and positive equilibriums of the considered system under stochastic perturbations are obtained. The research results are illustrated by numerical simulations. The proposed investigation procedure can be applied for arbitrary nonlinear stochastic delay differential equations with an order of nonlinearity higher than one. Copyright © 2016 John Wiley & Sons, Ltd.

Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimensionnonly need to solve one 4n-by-4nLMI. Numerical examples are presented to shown the effectiveness of our results.

Energy criterion of nonlinear stability of a flow of the Rivlin–Ericksen fluid in porous medium

Small-signal stability and decentralized control design for electric energy systems with a large penetration of distributed generators

Renewable Resources Management: Two Proposed Dynamic Optimal Control Models

This article deals with a numerical analysis of the static and dynamic performance of a compliant journal gas bearing. The common approach found in foil bearing literature consists in calculating the carrying capacity for a given shaft position. In this study the external load is fixed (magnitude and direction) and the related shaft position is investigated. Nevertheless, a rigid profile, able to support high imposed loads, is no longer valid if one considers that the bearing becomes compliant. An original calculation method of the initial profile considering rigid surfaces is proposed to overcome this problem. The prediction of nonlinear dynamic behavior, i.e., stability and response to external excitation, is investigated. Finally, a viscous damping model is introduced into the dynamic model in order to obtain the amount of structural damping necessary to increase the stability of the compliant journal gas bearing.

Gender differences in the perception of inflation

We investigate the behavior of several noisy nonlinear dynamical models in order to find out whether the presence of a common noise term may synchronize identical chaotic systems as recently supposed [S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1993); A. Maritan and J. R. Banavar, ibid. 72, 1451 (1994)]. The results of the present study show that noise can speed up orbit convergence in a restricted context, but in general cannot drive, by itself, a transition from chaotic to nonchaotic behavior. \textcopyright{} 1996 The American Physical Society.