Modeling of adulthood obesity in Spain using Itô-type stochastic differential equations

Abstract

Obesity is growing riskily in developed and developing countries. This should pose major concerns for the countries, not only from the health point, but also from the economic perspective. Our case study relies on the excess weight dynamics in Spain. The Spanish National Health Survey (ENSE) 2017 collects the percentage of overweight and obese adults in Spain from the year 1987 to 2017. A recent contribution proposed a nonautonomous compartmental system of ordinary differential equations to calibrate the incidence of excess weight in the Spanish adulthood population. Essentially, three principles were followed: the total adulthood population is time-dependent, the subpopulations interact homogeneously along the country, and excess weight plays the role of an infectious disease that is transmitted through contact by social pressure. Accounting for both data and model errors, frequentist nonlinear regression and Bayesian inference were conducted. The methods agreed well in terms of fit, prediction, bands and sensitivity analysis. In the present paper, the deterministic compartmental system of ordinary differential equations is randomized in a different manner, by employing Itô-type stochastic differential equations. The derivatives of the compartments are perturbed by Gaussian white noise-type pure errors that have a rough and unpredictable structure. From the Euler-Maruyama discretization, several strategies are utilized for estimating the parameters, based on the moments method and maximum likelihood estimation. Comparison is performed numerically by assessing the fit to the data.