we have an open question in front of us - has the transmission rate reduced because we've successfully reduced the spread during lockdown, or is the virus in truth running completely rampant and beyond our control, and actually burning out due to running up against herd immunity? we will need to see which hypothesis better fits the data, now. the health services aren't going to do that, but i will.
the various governments have given you their projections, in order to back up their argument for social distancing. this is generally done by fitting the curve to data in various existing jurisdictions, which introduces all of the specific bias in the various individual systems. this isn't an approach to determine the actual mortality rate via analysis and separation of the data, but rather an attempt to gather as many possible outcomes as possible, in order to create a set of bounds. in this thinking, the best case scenario is the best dataset we have, and the worst case scenario is the worst dataset we have - and careful analyses of biases in each of these specific data sets can happen later.
i think it's fair to state that everybody realizes that all of the data undercounts the number of mild cases, and consequently exaggerates the mortality rate. "canada's data will show those same biases", you say - and you're clearly correct, but that bias will appear in undocumented cases, not in exaggerated deaths.
i am going to rather construct a range of data by performing three simple calculations. this is my very basic model:
1) min range = [total population]*[66.66% infection rate, that is herd immunity]*[0.001]
2) average range = [total population]*[66.66% infection rate, that is herd immunity]*[0.003]
3) maximum range = [total population]*[66.66% infection rate, that is herd immunity]*[0.005]
you can do these calculations yourself, they're easy enough.
herd immunity levels should be empirically determined, not assumed, but the situation is not ideal. so, that's a source of error. some areas that lack resources and get overwhelmed may see numbers closer to the maximum range, which in north america would probably be a statement that relates better to the obese midwestern united states than the relatively healthy coasts, and the comparably fit & athletic canada.
if the data is better fit by my model than the official models, we should conclude that we are not experiencing disruptions in transmission at all, but have pretty much already all got it; that the reason hospitalization rates are going down is that we actually achieved herd immunity exceedingly quickly, despite our best efforts to prevent it. such a realization should have drastic implications for future public health policy.
what are my number of projected deaths in....
1) new york city: (5799, 17398, 28997) [projection: low end]
2) gta: (4133, 12399, 20665) [projection: low end]
3) montreal: (2800, 8399, 13999) [projection: low end]
4) detroit (metro area): (2866, 8599, 14332) [projection: expect something more like the middle number, due to higher comorbidity]
as you know, i've been leaning towards the low side of the calculation, but let's be rigorous here.
and, lets see where the numbers fall.