France continues to adjust their numbers to align with international standards, leading to a significant jump in reported cases today. That is not an actual growth in cases, just continuing to move to a new baseline. The change from yesterday is left blank today while they sort things out. Iran is coming in a little low today, but that could be noise. The other countries are all coming in as expected.
Switzerland continues to see a decline in active cases. This is from a roughly constant number of new infections being overwhelmed by a higher rate of people recovering. If the linear model continues (i.e. the number of new infections stays more or less constant) their active cases should continue to decrease more quickly over the next week, before slowing down to asymptotically approach a steady level where people recovery just as fast as they are catching the disease. Which is about as weird as it sounds. To take this out to the extreme, if nothing changes, that means that about 1000 new Swiss will be infected every day. The population of Switzerland is about 8.6 million people. Even if we are undercounting the number of cases by a factor of 10, that means it will take 8,600,000/10,000 = 860 days = 2.35 years for the entire country to be infected. That assumes that it hasn't mutated enough by then, so that a previous infection from COVID-19 means that your body is still immune to COVID-21.
The US isn't quite at a linear growth model yet but with a majority of the states with the most infections all imposing comprehensive stay-at-home orders, things are getting closer.
So what is causing the linear growth? According to research on Ebola from Maria Kiskowski and Gerardo Chowell, the transition from exponential to linear growth is expected as the disease is "saturating" the local communities. The disease then passes through in a "wave" or a "bubble" through the community, infecting new people only along the leading edge of the "bubble" while the interior is fully saturated. This would imply one (or more) local areas of high infection that are slowly working their way through a region. Events could happen where a bubble hits a kind of connectivity dead-end, or a particular connectivity crossroads could split off a second bubble, but the basic linear behavior is maintained.
If we follow this theory for what we are seeing with COVID-19, you can't consider a city or a neighborhood as a bubble. One idea then is that stay-at-home orders are reducing the number of interactions enough that these bubbles can form a saturated area in a fairly small region. Perhaps a single household is only interacting with a very few number of other households now, and a bubble can form out of just a few such households. A full cut-off from the rest of the world would cause the bubble to collapse, with nowhere left to go. However, occasional forays into 'necessary services' such as a grocery store could provide just enough exposure to inadvertently cause one more temporary link.
My problem with this theory applied to COVID-19 is that there is not just one bubble. Most states do not have any significantly high saturation counties, and nearly all infected states have at least a few cases in more than half of the counties. So that would mean bubbles would have to be tiny, and saturation areas would be being created and dry up all the time. That they would continue to cancel each other out equally is awfully convenient. It also implies that the type of stay-at-home order doesn't truly matter to connectivity, since not all states and counties are implementing the same thing. While this seems plausible for some epidemics, it doesn't seem like the full story for this situation.
Let me know your thoughts and ideas in the comments below. I'm interested to see if we can crowdsource an answer to this. Because I don't know about you, but I don't have 2.35 years of pasta stockpiled.
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