Pretty sure we decided that they fit a cubic to log(deaths), not to deaths. So log(deaths) goes to negative infinity as deaths goes to zero.
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Exactly. (I was trying to double-check that that was the case before you confirmed it for me.) One reason that a cubic model is dumb is that it's _incredibly_ sensitive to adding or changing a few points. A cubic model will _magnify_ small variations in recent data.
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But what they did on May 5 was fit a cubic to log(deaths), see that it went to negative infinity, and thus projected log(deaths) would go to negative infinity and thus deaths would go to zero.
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