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.

西班牙的超重人口正在危险地增长。西班牙国家健康调查2017证实了这一点，该调查收集了1987年至2017年西班牙超重和肥胖成年人的百分比。在本文中，我们提出了基于微分方程的数学模型，以校正西班牙成年后超重的发生率人口。主要原理是，肥胖是一种流行病，其存在三个阶段，即正常体重，超重和肥胖，健康个体可能会被社会接触所“感染”。我们从模型的适当确定性公式开始，其中通过最小化均方误差目标函数来拟合参数。该系统的长期行为表明，从长远来看，分别有37％和24％的西班牙成年人会超重和肥胖。由于对潜在现象和误差测量的不完全了解，必须将随机性纳入模型公式。因此，添加了白噪声误差项以进行非线性回归。响应变成一个随机过程，其预测间隔正确地捕获了超重和肥胖人群的变异性。通过将模型参数视为随机变量，我们迈出了一步。贝叶斯推理方法允许通过运行Metropolis算法（强力和自适应）来量化此设置下不确定性的传播。数值模拟表明，它提供了与频率分析相似的结果。不同方法的敏感性分析结果一致，表明预防策略比控制成人肥胖的治疗策略更为重要。特别是，从肥胖到超重阶段过渡的治疗对于减少肥胖病的流行是最不推荐的。