Have We Reached Herd Immunity?

I have been looking at the number of new cases per day, both for Santa Clara County and for the U.S., and the pattern is striking. Over the past month, number of new cases per day in the U.S. has gone down by a factor of about 2.4, for the county by a factor of about 3.5. Death rates are also down, although by much less, but one would expect death rates to lag case rates by a few weeks. I don't think the explanation can be the weather, since it's still winter.  I don't think it can be vaccination because there has not yet been enough of it to substantially affect the case rate.

The other obvious explanation is that the previous high was created by a lower level of precaution due to XMas and New Years. But that explains only a reduction in the rate of increase, not a reduction in the level, since all those people infected during the holidays were then around to infect other people. The fact that the level is falling means that each infected person is passing the infection on to fewer than one person, which is the definition of herd immunity.

If behavior is held constant, herd immunity ought to first appear as a constant rate of infection, each person passing the disease on to one other, then gradually become a shrinking rate. It looks as though we reached herd immunity under non-holiday behavior something close to two months ago, infection rates kept going up due to the holiday bump, and by the time that ended we were far enough into herd immunity (with non-holiday behavior) so that rates were falling. 

I was still surprised that they were falling so fast until I looked at how many cases had occurred recently. I haven't made an exact calculation, but it looks as though, for both the county and the country as a whole, the surge in cases over the two months of the peak  roughly doubled the cumulative total. It wouldn't be that surprising if that had pushed us well past the start of herd immunity.

There are two qualification to be made to the optimistic conclusion that the pandemic is almost over. One is that the requirement for herd immunity depends, among other things, on how people behave. If everyone concludes the pandemic is over and drops all precautions against passing on Covid, cases might start increasing again. The other is that there are at least two new variants of Covid now spreading through the U.S., and we cannot be sure that people immune to the old variant will be equally immune to the new. If, to take the most pessimistic possibility, the protection provided by having had Covid turns out to have no effect one of the variants, we are back to ground zero and in trouble.

My guess, however, is that neither will happen, and that in another few months the case rate will be back to last spring's lows. And falling.