Dengue fever has become one of the most outstanding infectious diseases in the world. Besides, the incidence and prevalence of dengue are increasing in the endemic areas of the tropical and subtropical regions. Space and time disease mapping models are common instruments to explain the patterns of disease counts, where hierarchical Bayesian models constitute a suitable framework for their formulation. These random events reflect interactions between nearby geographic locations, as well as correlations between close temporary instants. Functional data analysis techniques can better describe the evolution of disease mapping.

In this paper, the risk of dengue in Mexico, Central and South America is studied from a Functional approach through a Bayesian estimation model focused on Hilbert-valued autoregressive processes combined with the Kalman filtering algorithm. Thus, the temporal functional evolution of spatial geographic patterns of incidence risk in disease mapping during 1998-2018 is approximated. Applying this methodology, the excess of smoothing that occurs with traditional models is avoided and the heterogeneity is conserved across the years. It improves the number of false positives created by noise and the number of false negatives as well. The results obtained with the application of this model are compared with those of previous models, corroborating the preceding statements and obtaining better results in the relative risk estimates, providing greater robustness and stability of disease risk estimates.

登革热已成为世界上最杰出的传染病之一。此外，在热带和亚热带地区的流行地区，登革热的发病率和流行率正在增加。时空疾病图谱模型是解释疾病计数模式的常用工具，其中分级贝叶斯模型构成了其制定的合适框架。这些随机事件反映了附近地理位置之间的相互作用以及临近的临时时刻之间的相关性。功能数据分析技术可以更好地描述疾病图谱的演变。

在本文中，通过基于贝叶斯估计模型的功能性方法，重点研究了希尔伯特值自回归过程并结合卡尔曼滤波算法，从而研究了墨西哥，中美洲和南美洲的登革热风险。因此，可以估算出1998-2018年疾病分布图中发病风险的空间地理格局的时空演变。应用这种方法，可以避免传统模型中出现的过度平滑现象，并且多年来可以保持异构性。它改善了由噪声产生的误报的数量以及误报的数量。将应用此模型获得的结果与以前的模型进行比较，以证实前面的陈述并在相对风险估计中获得更好的结果，