Dengue in Brazil: Regression and probabilistic modeling

The work aimed to adjust Poisson models and their generalizations (Quasi-Poisson and Negative Binomial) to the behavior of the number of dengue cases grouped in Recife-PE. Weekly epidemiological records of dengue were used, from 2009 to 2018, and they were made available through the Citizen Information Service. Initially, Poisson models and their generalizations were applied, followed by a diagnostic analysis of the residuals, using influence measures, in order to analyze how much a specific observation affects some property of the studied model. The adjustment results indicated that the Negative Binomial model showed a satisfactory adjustment, compared to other models for description of the data, minimizing dispersions parameters more accurately. Regarding the analysis of the residuals, it can be stated that the assumptions of normal distribution and homogeneity of the residuals in the Generalized Linear Models (GLM) were provided. In addition, the existence of atypical and influential values was verified, which should be examined carefully. Therefore, it can be concluded that diagnosis is an important tool for researchers, in which they present basic premises for the reliability of the GLM, data set, and goodness of fit. Finally, we point out that more scientific studies are needed, in this context, to have more consistency in this application.