The modelling being used by the UK government for policy making has been published here:
https://www.imperial.ac.uk/media/im...-College-COVID19-NPI-modelling-16-03-2020.pdf
It is not pretty, but the modelling methods seem sensible. Main recommendation is for disruptive interventions (self quarantine, social distancing and school shutdowns) to be used in phases triggered on and off by rises in demand for hospital beds. This lasts until a vaccine is developed and will be in place for about 60-70% of the time.
They did not model a total lockdown.
The idea is that you can't maintain lockdowns of disruptive interventions for long, and it returns after lockdowns are lifted. So instead, you intervene when cases begin to rise and lift when they drop. This keeps the health system working and casualties low.
But it's based on some uncertain assumptions about the effectiveness of each measure. It's not quite "numbers pulled from my arse", but no one really knows what the effectiveness of these measures is or how many people will ignore them
However, the modelled inputs were designed to assume a relatively low effectiveness of each measure and relatively high degree of quarrantine-breaking.
Do nothing is and Speedrun for herd immunity is 550,000 deaths...
But that did not model the collapse of the health system and assumes we build and train 30 times or current ICU capacity to cope - within 3 months.
The model suggests we can reduce deaths to 20 or 30 thousand if we keep intermittently crushing the growth curve with targeted interventions, and we would just about be within our ICU capacity.
The trigger for these measures would be 200 COVID patients in ICU, which I expect we are very close to hitting.
They also modelled the USA, but it's mostly in an appendix that I haven't read yet. I think the conclusions are similar to the UK. USA is only slightly protected by it's lower population density and larger distances that reduce travel.