What's the evidence for "flattening the curve" by social distancing measures in the context of contagious respiratory diseases?

Question

This is more of Skeptics-style question, but since I only know of people on Stack Exchange challenging this (so it would not be a "notable claim" for Skeptics)... I'm asking here.

For context as what we're talking about, I'll recall that

In epidemiology, the curve refers to the projected number of new cases over a period of time.

In contrast to a steep rise of coronavirus infections, a more gradual uptick of cases will see the same number of people get infected, but without overburdening the health-care system at any one time.

The idea of flattening the curve is to stagger the number of new cases over a longer period, so that people have better access to care.

Some people challenge that social distancing measures like banning public gatherings etc. are truly effective at reducing the transmission of contagious respiratory diseases like influenza. (I'd link you the Politics SE questions on this, but most such questions got deleted over there for being off-topic and the askers told to ask here... which for some reasons none of them seem to do.)

So what is some convincing evidence from past epidemics that such social distancing measures are effective at "flattening the curve"?

Answer 1

There actually numerous documents discussing the matter but one moderately cited paper (~300 citations) Hatchett et al. (2007) compared the responses on US cities during the 1918 influenza:

Nonpharmaceutical interventions (NPIs) intended to reduce infectious contacts between persons form an integral part of plans to mitigate the impact of the next influenza pandemic. Although the potential benefits of NPIs are supported by mathematical models, the historical evidence for the impact of such interventions in past pandemics has not been systematically examined. We obtained data on the timing of 19 classes of NPI in 17 U.S. cities during the 1918 pandemic and tested the hypothesis that early implementation of multiple interventions was associated with reduced disease transmission. Consistent with this hypothesis, cities in which multiple interventions were implemented at an early phase of the epidemic had peak death rates ≈50% lower than those that did not and had less-steep epidemic curves. Cities in which multiple interventions were implemented at an early phase of the epidemic also showed a trend toward lower cumulative excess mortality, but the difference was smaller (≈20%) and less statistically significant than that for peak death rates. This finding was not unexpected, given that few cities maintained NPIs longer than 6 weeks in 1918. Early implementation of certain interventions, including closure of schools, churches, and theaters, was associated with lower peak death rates, but no single intervention showed an association with improved aggregate outcomes for the 1918 phase of the pandemic. These findings support the hypothesis that rapid implementation of multiple NPIs can significantly reduce influenza transmission, but that viral spread will be renewed upon relaxation of such measures.

A 2014 UK government (72-page) review focused only on mass gatherings, was somewhat more circumspect in its conclusions:

In conclusion there is limited data indicating that mass gatherings are associated with influenza transmission and this theme is continued with the inclusion of new evidence for the update. Certain unique events such as the Hajj, specialised settings including civilian and military ships- a new theme for this update, indoor venues and crowded outdoor venues provide the primary evidence base to suggest mass gatherings can be associated with Influenza outbreaks. Some evidence suggests that restricting mass gatherings together with other social distancing measures may help to reduce transmission. However, the evidence is still not strong enough to warrant advocating legislated restrictions. Therefore, in a pandemic situation a cautious policy of voluntary avoidance of mass gatherings would is still the most prudent message. Operational considerations including practical implications of policy directed at restricting mass gathering events should be carefully considered