Given all the limits described, assuming an uniform distribution of people's behavior, our math model predicts poor performance of any kind of BLE contact tracing app.
What do we mean by effectiveness: 100% effectiveness means that, on average, if anyone turned to be infected, all the people who had previous contact with him would be track back and warned. With 50% we would be only able to reach half of them.
Given app adoption of 43% and a global market share of 25 % iOS and 75% Android*, define average contact time as the average of minutes that two people are in proximity.
10.40% effectiveness
We obtain 10.40% effectiveness if we consider the average contact time is 15 minutes, and the Android app will run in foreground for 10% of the time. Effectiveness would drop to 3.47% if we account an average contact time of 5 minutes.
Increasing the app adoption from 43% to an incredibly high 60% will increase the effectiveness to 6.75% and 20.25% for an average contact time of 5 and 15 minutes respectively.
In US, given a lower trust in their government and higher iOS share, the effectiveness can be as low as 1%.
Considering that current deployed solutions can hardly overcome such limitations, we don’t understand how those apps can have a real impact.
We suspect that most of the news and the political communications we read so far, could have been misled by a generalized and natural optimism, the same we did in the very beginning of our study.
Nevertheless, this approach can still have a value if it will be possible to overcome the previous three drops of the effectiveness.
If we could be able to remove all the existing limitation, the theoretical limit would be the square of the adoption rate.
Unfortunately, this is something that only Apple and Google can do. And they have necessarily to do it together.