Not so long ago, Vallance claimed that there could be about 1,000 cases of COVID-19 for every current death in the UK. Now, the Italian death rate (as a percentage of reported cases) is extremely high, and it might also be high as a percentage of true cases including unreported. But if Vallance's estimate applies here too, the 7000 deaths there so far would imply 7 million cases, a little over 10% of their population. This is just about enough to significantly bend the exponential curve as it implies an actual infection rate of under 90% of R0 (ie, something more like 2.3 new infections per case rather than 2.6).
Of course it would be a bit longer before that fed through into the observed fatality rate and with reported cases clearly under-counting by a huge factor, it's not something we could know about for a while. The slight slowdown in death rate being observed now cannot possibly be evidence of this theory yet.
Kucharski estimates a factor of 20 in the under-counting which would mean about 2% incidence rate, still a couple of doublings away from that point.
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