A conformable mathematical model for alcohol consumption in Spain

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.

We investigate the dynamics of a delayed stochastic mathematical model to understand the evolution of the alcohol consumption in Spain. Sufficient condition for stability in probability of the equilibrium point of the dynamic model with aftereffect and stochastic perturbations is obtained via Kolmanovskii and Shaikhet general method of Lyapunov functionals construction. We conclude that alcohol consumption in Spain will be constant (with stability) in time with around 36.47% of nonconsumers, 62.94% of nonrisk consumers, and 0.59% of risk consumers. This approach allows us to emphasize the possibilities of the dynamical models in order to study human behaviour.

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.

Uncertain inverse problem for fractional dynamical systems using perturbed collage theorem

In this paper, the conformable fractional-order SIR epidemic model are solved by means of an analytic technique for nonlinear problems, namely, the conformable fractional differential transformation method (CFDTM) and variational iteration method (VIM). These models are nonlinear system of conformable fractional differential equation (CFDE) that has no analytic solution. The VIM is based on conformable fractional derivative and proved. The result revealed that both methods are in agreement and are accurate and efficient for solving systems of OFDE.

An approximation solution of a nonlinear equation with Riemann–Liouville's fractional derivatives by He's variational iteration method

We consider a SEIR model for the spread (transmission) of an infectious disease. The model has played an important role due to world pandemic disease spread cases. Our contributions in this paper are three folds. Our first contribution is to provide successive approximation and variational iteration methods to obtain analytical approximate solutions to the SEIR model. Our second contribution is to prove that for solving the SEIR model, the variational iteration and successive approximation methods are identical when we have some particular values of Lagrange multipliers in the variational iteration formulation. Third, we propose a new multistage-analytical method for solving the SEIR model. Computational experiments show that the successive approximation and variational iteration methods are accurate for small size of time domain. In contrast, our proposed multistage-analytical method is successful to solve the SEIR model very accurately for large size of time domain. Furthermore, the order of accuracy of the multistage-analytical method can be made higher simply by taking more number of successive iterations in the multistage evolution.

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiency and convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partial differential equations usually needs a coordinate transformation in order to discard the singularity of the partial differential equation. Most often this transformation is not applicable and even does not exist. Therefore in this case the solution for the singular partial differential equation does not exist. In the present study the results of simulation for the singular partial differential equations with variable coefficients using the Fourier transform variational iteration method are compared with the results of simulation using the modified variational iteration method. The comparison shows that the effectiveness and accuracy of Fourier transform variational iteration method is more than that of the modified variational iteration method for the simulation of singular partial differential equations.

The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method

In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given.

Exact solutions of nonlinear diffusion equations by variational iteration method

In this article, contact problem with fractional derivatives is studied. We use fractional derivative in the sense of Caputo. We deploy penalty function method to degenerate the obstacle problem into a system of fractional boundary value problems (FBVPs). The series solution of this system of FBVPs is acquired by using the variational iteration method (VIM). The performance as well as precision of the applied method is gauged by means of significant numerical tests. We further study the convergence and residual errors of the solutions by giving variation to the fractional parameter, and graphically present the solutions and residual errors accordingly. The outcomes thus obtained witness the high effectiveness of VIM for solving FBVPs.

Periodic solutions for some strongly nonlinear oscillations by He’s variational iteration method