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.
