Computational modeling of epidemiological count data using Non-Homogeneous Poisson Processes and functional data

In this work, we introduce a novel methodology for modeling discrete count variables within the framework of stochastic processes. Our approach integrates two statistical areas: Non-Homogeneous Poisson Processes for the estimation and prediction of intensity functions based on explanatory variables and functional data estimation techniques. Through a comprehensive case study focusing on an infectious disease with viral characteristics, we demonstrate the potential of our methodology. We provide empirical evidence that our methodology offers a robust alternative for modeling count variables. Our findings support the utility of our approach in capturing the complex dynamics inherent in count data in infectious disease epidemiological phenomena.