0000000000013976
AUTHOR
Rafael J. Villanueva
A probabilistic estimation and prediction technique for dynamic continuous social science models: The evolution of the attitude of the Basque Country population towards ETA as a case study
In this paper, a computational technique to deal with uncertainty in dynamic continuous models in Social Sciences is presented.Considering data from surveys,the method consists of determining the probability distribution of the survey output and this allows to sample data and fit the model to the sampled data using a goodness-of-fit criterion based the χ2-test. Taking the fitted parameters that were not rejected by the χ2-test, substituting them into the model and computing their outputs, 95% confidence intervals in each time instant capturing the uncertainty of the survey data (probabilistic estimation) is built. Using the same set of obtained model parameters, a prediction over …
Using random networks to study the dynamics of respiratory syncytial virus (RSV) in the Spanish region of Valencia
[EN] Seasonal fluctuations in the incidence of several respiratory infections are a feature of epidemiological surveys all around the world. This phenomenon is characteristic of influenza and respiratory syncytial virus pandemics. However, the explanation of the seasonal outbreaks of these diseases remains poorly understood. Many statistical studies have been carried out in order to provide a correlation of the outbreaks with climatic or social factors without achieving a definitive conclusion. Here we show that, in a random social network, self-sustained seasonal epidemics emerge as a process modulated by the infection probability and the immunity period after recovering from the infection…
Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach
Due to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of these equations when the random inputs follow standard probability distributions. But in many cases these random inputs do not have a standard probability distribution. In this paper, we present a step-by-step constructive methodology to implement directly a useful version of adaptive gPC for arbitrary distributions, extending the applicability of the gPC. The paper mainly focuses on the computation…
Optimizing strategies for meningococcal C disease vaccination in Valencia (Spain)
Background: Meningococcal C (MenC) conjugate vaccines have controlled invasive diseases associated with this serogroup in countries where they are included in National Immunization Programs and also in an extensive catch-up program involving subjects up to 20 years of age. Catch-up was important, not only because it prevented disease in adolescents and young adults at risk, but also because it decreased transmission of the bacteria, since it was in this age group where the organism was circulating. Our objective is to develop a new vaccination schedule to achieve maximum seroprotection in these groups. Methods: A recent study has provided detailed age-structured information on the seroprote…
Modelling the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia: an epidemiological approach with uncertainty
Student academic underachievement is a concern of paramount importance in Europe, where around 15% of the students in the last high school courses do not achieve the minimum knowledge academic requirement. In this paper, we propose a model based on a system of differential equations to study the dynamics of the students academic performance in the German region of North Rhine-Westphalia. This approach is supported by the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. This model allows us to forecast the student academic performance by means of confidence intervals over the next few years.
Analysing the effect of public health campaigns on reducing excess weight: a modelling approach for the Spanish Autonomous Region of the Community of Valencia.
Abstract Excess weight is fast becoming a serious health concern in the developed and developing world. The concern of the public health sector has lead to the development of public health campaigns, focusing on two-fold goals: to inform the public as to the health risks inherent in being overweight, and the benefits of a change in nutritional behaviour. Recent studies indicate that the effects of the average public health campaign on the target community is around 5%. In this study we aim to quantify the effect of different public health campaigns on lifestyle behaviour in the target populations in order to bring about weightloss in a significant number of people over the next few years. T…
Probabilistic European Country Risk Score Forecasting Using a Diffusion Model
Over the last few years, global crisis has shaken confidence in most European economies. As a consequence, a lack of confidence has spread amongst European countries leading to Europe’s financial instability. Therefore, forecasting the next future of economic situation involves high levels of uncertainty. In this respect, it would be interesting to use tools which allow to predict the trends and evolution of each country’s confidence rating. The Country Risk Score (CRS) represents a good indicator to measure the current situation of a country regarding measures of economic, political and financial Risk in order to determine country Risk ratings. CRS is underscored by Euromoney Agency and is…
Non-parametric probabilistic forecasting of academic performance in Spanish high school using an epidemiological modelling approach
Academic underachievement is a concern of paramount importance in Europe, and particularly in Spain, where around of 30% of the students in the last two courses in high school do not achieve the minimum knowledge academic requirement. In order to analyse this problem, we propose a mathematical model via a system of ordinary differential equations to study the dynamics of the academic performance in Spain. Our approach is based on the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. Moreover, in order to consider the uncertainty in the estimation of model parameters, a bootstrapping approach is employed. This technique permits to for…
Solving continuous models with dependent uncertainty: a computational approach
This paper presents a computational study on a quasi-Galerkin projection-based method to deal with a class of systems of random ordinary differential equations (r.o.d.e.'s) which is assumed to depend on a finite number of random variables (r.v.'s). This class of systems of r.o.d.e.'s appears in different areas, particularly in epidemiology modelling. In contrast with the other available Galerkin-based techniques, such as the generalized Polynomial Chaos, the proposed method expands the solution directly in terms of the random inputs rather than auxiliary r.v.'s. Theoretically, Galerkin projection-based methods take advantage of orthogonality with the aim of simplifying the involved computat…
Modeling and predicting the Spanish Bachillerato academic results over the next few years using a random network model
[EN] Academic performance is a concern of paramount importance in Spain, where around of 30% of the students in the last two courses in high school, before to access to the labor market or to the university, do not achieve the minimum knowledge required according to the Spanish educational law in force. In order to analyze this problem, we propose a random network model to study the dynamics of the academic performance in Spain. Our approach is based on the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. Moreover, in order to consider the uncertainty in the estimation of model parameters, we perform a lot of simulations taking as t…
Forecasting Latin America’s Country Risk Scores by Means of a Dynamic Diffusion Model
Over the last years, worldwide financial market instability has shaken confidence in global economies. Global financial crisis and changes in sovereign debts ratings have affected the Latin American financial markets and their economies. However, Latin American s relative resilience to the more acute rise in risk seen in other regions like Europe during last years is offering investors new options for improving risk-return trade-offs. Therefore, forecasting the future of economic situation involves high levels of uncertainty. The Country Risk Score (CRS) represents a broadly used indicator to measure the current situation of a country regarding measures of economic, political, and financial…
Solving a model for the evolution of smoking habit in Spain with homotopy analysis method
We obtain an approximated analytical solution for a dynamic model for the prevalence of the smoking habit in a constant population but with equal and different from zero birth and death rates. This model has been successfully used to explain the evolution of the smoking habit in Spain. By means of the Homotopy Analysis Method, we obtain an analytic expression in powers of time t which reproduces the correct solution for a certain range of time. To enlarge the domain of convergence we have applied the so-called optimal convergence-control parameter technique and the homotopy-Padé technique. We present and discuss graphical results for our solutions. ©
epiModel: A system to build automatically systems of differential equations of compartmental type-epidemiological models
In this paper we describe epiModel, a code developed in Mathematica that facilitates the building of systems of differential equations corresponding to type-epidemiological linear or quadratic models whose characteristics are defined in text files following an easy syntax. It includes the possibility of obtaining the equations of models involving age and/or sex groups. © 2011.
The dynamics over the next few years of the Spanish mobile telecommunications market share: a mathematical modelling approach
Taking into account available data from 2002 to 2009 about the market share percentages of the Spanish mobile telecommunications service providers, a dynamic diffusion model to study the evolution of the clients’ change between the different companies during the period 2010–2016 is proposed. The constructed model provides a tool for forecasting short-term trends about the customers’ preferences with respect to mobile network operators taking into account both, autonomous decisions due to direct marketing and advertising strategies, and also decisions adopted through interaction via social influence. The model can provide insights to companies for designing strategies in order to gain market…
A deterministic model for highly contagious diseases: The case of varicella
[EN] The classic nonlinear Kermack-McKendrick model based upon a system of differential equations has been widely applied to model the rise and fall of global pandemic and also seasonal epidemic by introducing a forced harmonic infectivity which would change throughout the year. These methods work well in their respective domains of applicability, and for certain diseases, but they fail when both seasonality and high infectivity are combined. In this paper we consider a Susceptible-Infected-Recovered, or SIR, model with two latent states to model the propagation and evolutionary history of varicella in humans. We show that infectivity can be calculated from real data and we find a nonstanda…
Mathematical modelling of social obesity epidemic in the region of Valencia, Spain
In this article, we analyse the incidence of excess weight in 24- to 65-year-old residents in the region of Valencia, Spain, and predict its behaviour in the coming years. In addition, we present some possible strategies to prevent the spread of the obesity epidemic. We use classical logistic regression analysis to find out that a sedentary lifestyle and unhealthy nutritional habits are the most important causes of obesity in the 24- to 65-year-old population in Valencia. We propose a new mathematical model of epidemiological type to predict the incidence of excess weight in this population in the coming years. Based on the mathematical model sensitivity analysis, some possible general stra…
The effect of the Spanish Law of Political Parties (LPP) on the attitude of the Basque Country population towards ETA: A dynamic modelling approach
Abstract In June 2002, the Spanish Government passed the “Law of Political Parties” (LPP) with the aim, among others, of preventing parties giving political support to terrorist organizations. This law affected the Basque nationalist party “Batasuna”, due to its proved relation with ETA. In this paper, taking data from the Euskobarometro (Basque Country survey) related to the attitude of the Basque population towards ETA, we propose a dynamic model for the pre-LPP scenario. This model will be extrapolated to the future in order to predict what would have happened to the attitude of the Basque population if the law had not been passed. These model predictions will be compared to post-LPP dat…