The study of infectious disease behavior has been a scientific concern for many years as early identification of outbreaks provides great advantages including timely implementation of public health measures to limit the spread of an epidemic. We propose a methodology that merges the predictions of (i) a computational model with machine learning, (ii) a projection model, and (iii) a proposed smoothed endemic channel calculation. The predictions are made on weekly acute respiratory infection (ARI) data obtained from epidemiological reports in Mexico, along with the usage of key terms in the Google search engine. The results obtained with this methodology were compared with state-of-the-art techniques resulting in reduced root mean squared percentage error (RMPSE) and maximum absolute percent error (MAPE) metrics, achieving a MAPE of 21.7%. This methodology could be extended to detect and raise alerts on possible outbreaks on ARI as well as for other seasonal infectious diseases.