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During the the COVID-19 pandemic, mathematical models tended to over-project the epidemic waves. At the beginning of the pandemic, modelling groups around the world projected that, if no public health responses are implemented, over 60% of the population will be infected. In recent model projections for the 4th waves, a similar figure of over 60% of the unvaccinated and partial vaccinated population will be infected. This level of projection seem to run contrary to real pandemics in history and recent times. 

An examination of the well known final-size formula for standard epidemic  models provide a reason for the over-projections; when the basic reproduction number R0 is around 2, the infected proportion will be over 80% by the final size formula,  and the susceptible population has to decline about 50% for the the epidemic to peak. This begs for discussions on two kinds of questions: (1) What other drivers need to be considered,  in addition to the decline of susceptible population, to understand why and when real epidemics peak  and then fall? (2) How do we adapt the standard epidemic models to make reliable predictions  of real epidemics.

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