Mathematical modeling of adulthood obesity epidemic in Spain using deterministic, frequentist and Bayesian approaches

The excess weight population is growing riskily in Spain. This is confirmed by the Spanish National Health Survey 2017, which gathers the percentage of overweight and obese adults in Spain from 1987 to 2017. In this paper we propose a mathematical model based on differential equations to calibrate the incidence of excess weight in the Spanish adulthood population. The main principle is that fatness is an epidemic, where there are three stages, namely normal weight, overweight and obese, and healthy individuals may become “infected” by social contact. We start with a well-posed deterministic formulation of the model, where the parameters are fitted by minimizing the mean square error objective function. The long-term behavior of the system shows that 37% and 24% of Spanish adults will be overweight and obese in the long run, respectively. Due to the incomplete knowledge of the underlying phenomenon and error measurements, randomness must be incorporated into the model formulation. A white noise error term is thus added to conduct nonlinear regression. The response becomes a stochastic process, whose prediction interval captures the variability of the overweight and obese populations correctly. We go a step beyond by treating the model parameters as random variables. The Bayesian inference method allows for quantifying the propagation of uncertainty in this setting, by running the Metropolis algorithm (both brute-force and Adaptive). The numerical simulations show that it provides similar results to the frequentist analysis. The sensitivity analyses from the different methods agree and suggest that prevention strategies are more important than treatment strategies to control adulthood obesity. Specially, the treatment of the transition from the obese to the overweight stages is the least recommendable for reducing the obesity epidemic.