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A lot of people are commenting on this, I have some thoughts.
First, privacy: there's no way in hell the NY Times got access to raw individual cell phone data. This was almost certainly based on anonymized, aggregated data. Note that map is county coded, which is likely how the Times received it from cell providers.
*or possibly apps that have access to location; still, no privacy issues if provided in anonymized, aggregated form. Let's say you live in Acme County, Pennsyltucky. The Times might know total before/after travel for everybody in Acme County, but no idea where you've been.
OK, secondly: in order to do this kind of analysis you have to define "travel." A phone has a primary location (home), now you have to define what constitutes travel. Is it >0.25 miles from home? 0.5 miles? 1 mile? 10 miles?
Given a definition of travel, you could ask a cell company or app to provide you, for example, the percent of user phones were in a "travel" state in time period 1, and in time period 2, at the US county level, with no big privacy issues.
For example suppose we had a table of aggregated pre and post period % of time "traveling" for all US counties:

COUNTY PRE POST
Cook County, IL 25% 2%
Acme, Pennsyltucky 40% 25%

This is likely the basis of the heat-coded map.
Now, third: obviously it's one thing to stay within 1, or 2, or 5 miles of home if you live in the Northside of Chicago, and something different if you live in Hooterville, Acme County Pennsyltucky.
Especially if Hooterville has no grocery stores or doctors, and the nearest Casey's is 12 miles away in Bugtussle. There is travel, and there is essential travel. The folks in Hooterville aren't out joyriding around to various packed street carnivals.
But I suppose this map gives a certain level of comforting smug self-righteousness to the Times and their cosmopolitan urban reader base. When you're locked down in your 700 sqft hi-rise apartment, it's nice to know those idiot rural rubes are the real virus villains.
Finally, I want you to imagine another county coded heat map. Sure, virus spread is a function of travel; but moreso a function of where you live, where you travel, their population densities, and especially their densities of virus carrier.
Example: my son lives in a 28-story apartment tower in Chicago with 400 other people. My sister lives in a Hooterville and must travel 14 miles for groceries or to see a doctor. Also there's probably no confirmed Covid cases within 50 miles of her.
My son is completely "sheltered in place" and reduced his travel 100%, but simply going to the little lobby grocery store, getting his mail, or even breathing inside his apartment puts him at some risk of virus exposure.
By contrast my sister has reduced her "travel" by maybe 25%, because the rest of it she can't. And even that necessary travel from Hooterville to the bright lights of Bugtussle exposes her to far less virus risk than my son simply staying inside his apartment.
So I would propose an alternate map: define geolocation by virus risk. It's possible to denote a location by proximity to the nearest confirmed virus case, or number of virus cases within a 1 mile, 5 mile, etc. radius, Now you can define *risky* travel.
For example, you could compare the virus risk of home location vs the virus risk of where they travel, for pre (let's say 3/1-3/15) and post (3/16-3/30) lockdown periods. In other words, how much time was spent in locations with high or higher risk of virus exposure?
I suspect that map would reveal that while travel hasn't been reduced much in rural locales, much of the travel is from low risk to slightly higher but still low risk areas. Urbanites may have cut down travel completely, but maybe it was between high risk and high risk locations.
In conclusion, data is like a street lamp; it can be useful for illumination, but it can also be useful for drunks to cling on.
Addendum: what would be illuminating is a map of the probability of being exposed (visiting a location that was within 10 feet of a virus carrier in the previous hour), broken down by home location, week, and essential (work, medical, provisions) or non-essential travel.
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