Non-Homogeneous Poisson Process & Functional Data: A procedure for infectious diseases count data modeling

In some epidemiological studies it is of interest to observe the behavior of the number of cases of a disease in a population, such as Dengue, Zika, Covid-19, among others; in order to predict the evolution of future cases. In this study, we propose to combine Non-Homogeneous Poisson Processes (NHPP) and Functional Data Analysis (FDA) methodologies for count-data prediction. We consider cumulative cases, subjected to time evolution and influence of explanatory variables. The proposed procedure allows to estimate the most representative cumulative-cases trajectory included its non-parametric confidence bands, as well as detect possible outlier trajectories, and predict future cumulative counting. An application with real infectious diseases data is also presented.