  Compartmental equations are primary tools in disease spreading studies. Their
predictions are accurate for large populations but disagree with empirical and
simulated data for finite populations, where uncertainties become a relevant
factor. Starting from the agent-based approach, we investigate the role of
uncertainties and autocorrelation functions in SIS epidemic model, including
their relationship with epidemiological variables. We find new differential
equations that take uncertainties into account. The findings provide improved
predictions to the SIS model and it can offer new insights for emerging
diseases.
