Simple exposure is not enough to become immune. You need a significant infection which triggers a strong immune system response to build long term immunity. Thus in the initial stages of an outbreak you can basically ignore people that became infected weeks ago, had a significant infection, and are now immune due to the exponential growth curve.

It’s only after the rate of infection stayed the same or falls for a month+ that you need to adjust for such people.

>You need a significant infection which triggers a strong immune system response to build long term immunity.

I don't think this is true. I get the flu shot every year and have never had a strong immune response to it, yet I'm still immune to the major flu strains each year.

Point being, it's possible for your body to create long term immunity to a virus without suffering from a severe infection.

I am specifically referring to COVID-19 where we don’t have a vaccine. Vaccines fake a significant infection to get that same strong immune response. This is also why some vaccines require multiple doses over a short period.

If we did know the true current infection rate (which this report does not give, as there are too many unresolved assumptions), then could we not, with some reasonable assumptions about the rate of spread and the duration of an infection, estimate the number who have recovered from it?

I think that requires an antibody test

Indeed PCR tests only test for the presence of the virus itself. Their big advantage is an extremely high specificity. Antibody tests are plagued by large numbers of false positives.