Discrete time forecasting of epidemics

Forecasting in the domain of infectious diseases aims at estimating the number of cases ahead of time during an epidemic, hence fundamentally requires understanding its dynamics. In fact, estimates about the dynamics help to predict the number of cases in an epidemic, which will depend on determining a few of defining factors such as its starting point, the turning point, growth factor, and the size of the epidemic in total number of cases. In this work a phenomenological model deals with a practical aspect often disregarded in such studies, namely that health surveillance produces counts in batches when aggregated over discrete time, such as days, weeks, months, or other time units. This model enables derivation of equations that permit both estimating key dynamics parameters and forecasting. Results using both severe acute respiratory illness data and synthetic data show that the forecasting follows very well over time the dynamics and is resilient with statistical noise, but has a delay effect due to the discrete time.