Here we answer some of your questions we received by email.

Q1. How can we estimate the hospital capacity?

The SIR equations do not distinguish between infected individuals that require hospitalization and those who don't. Since hospital capacity is a fundamental component of 'flatten the curve', I addressed this question by using an 'SIHR' model to distinguish between infected people that require critical care (H) and those who do not (I).

The top panel on the right shows the percentage of the population that is infected at a given time, while the middle panel shows the percentage of the population that requires critical care. Note that both graphs have nearly the same shape, but that the percentage of people requiring critical care at any time is much smaller (<0.3% of the population).

In terms of what you can 'flatten', as the average citizen it is unlikely that you will require critical care, so you can flatten the infections curve (the top panel). However, a consequence of flattening the infections curve is to also flatten the critical care curve (the middle panel). This is central to the idea of flattening the curve: we implement social distancing not necessarily to protect ourselves, but to protect the most vulernable.

The hospital capacity line is relevant to the percentage of the population requiring critical care; the default value shows hosptial capacity as 0.2% of the population, i.e, if more than 2 out of every 1000 people require critical care, then hospital capacity is exceeded. Admittedly, this sounds like a very well-funded healthcare system, so please see the 'More models' tab to understand that the numbers generated by this app should not be taken too literally.

Q2. What does social distancing equal to 20% mean?

For COVID-19, a contact is defined as coming within 1-2m of another person. Therefore, if at your baseline level (social distancing =0%) you contacted 50 people each day, social distancing at 20% means that you reduce your contacts to 80% of your baseline level (=40 people per day). Please remember that you are not supposed to take these numbers too literally: many of the graphs here suggest that social distancing at 20% will prevent hospital overload: these models are too simple for their results to be understood that precisely (see the 'More models' tab).

My answer above is not very good. What about becoming infected via touching a contaminated surface? What about touching a contaminated surface 1 day after the contamination? And what about coming into contact with someone else for 1 minute vs. 1 hour? These details should matter, but classically this component of epidemiological models has been difficult to pin down.