4 ms·

A network-based explanation of why most Covid-19 infection curves are linear

16 points by viburnum 6y ago

tduberne 6y ago
Really interesting paper. Layman summary for those not used to network science: infection rate are lower than expected from standard models, because they consider each infected person meets new completely random strangers, while in reality, they are more likely to meet those who infected them, or those who infected those who infected them. In particular, the paper shows that a "phase transition" happens when the degree (average number of person met per person) exceeds a threshold, which the paper estimates to be around 7. Above that threshold, growth becomes exponential rather than linear.
fargle 6y ago
Mar's law. Rule 6 of Akin's Laws of Spacecraft Design: 6. Everything is linear if plotted log-log with a fat magic marker. http://spacecraft.ssl.umd.edu/akins_laws.html http://spacecraft.ssl.umd.edu/akins_laws.html
- rrobukef 6y ago
  No log-log plots nor fat magic markers in this paper though.
rrobukef 6y ago
Wonderful paper! I wonder if amateur real-world simulations are possible based on public data (streets, population density, daily movement). The computing power needed for 100,000 nodes, ~8 edges, ~30-60 sim. days, >>100 experiments seems fairly limited. An estimated 5 GFLOP should be possible for a desktop in reasonable time.
scoot_718 6y ago
Most of the Covid infection curves I've seen are linear because the scales are logarithmic.
derbOac 6y ago
This is a really great paper but I thought there was a general move to network-based models anyway? I recall it coming up during quarantine policy discussions. Nice work though. It seems more practically evident to me now than early on. In my area, the returning growth seems driven by medium sized clusters that are scattered geographically and aren't the same as what you might have thought early on, in that it's not spreading evenly in densely populated areas.
lmilcin 6y ago
I don't think it's true. I believe the reason we have linear or stable infection rates is that the determination to stop the virus grows as the number grow and then wanes as infection rates fall. This basically works like a thermostat (viro-stat?) and is due to governments or large parts of population not willing to put up with restriction when rates are falling ("why do I need to comply, this is no longer a real problem?") This is what I see here in Poland. The government supposedly "closely" watches the situation and puts new restriction wherever the infection rates spike but then promptly removes them when they start falling to what is described as "acceptable level". This is no way to combat the virus, this is the recipe to keep it around indefinitely.
gnusty_gnurc 6y ago
Michael Levitt has been arguing covid-19 never experiences the apocalyptic exponential growth that most people/media seem to think is going on. With a Gompertz curve, we start out with very high growth in the beginning but the growth constantly declines from the outset. Even the idea of network-based analysis and heterogeneity was something he talked about back in March or thereabouts IIRC. https://www.medrxiv.org/content/10.1101/2020.06.26.20140814v2 https://www.medrxiv.org/content/10.1101/2020.06.26.20140814v...

16 points by viburnum 6y ago

Really interesting paper. Layman summary for those not used to network science: infection rate are lower than expected from standard models, because they consider each infected person meets new completely random strangers, while in reality, they are more likely to meet those who infected them, or those who infected those who infected them. In particular, the paper shows that a "phase transition" happens when the degree (average number of person met per person) exceeds a threshold, which the paper estimates to be around 7. Above that threshold, growth becomes exponential rather than linear.

fargle 6y ago

Mar's law. Rule 6 of Akin's Laws of Spacecraft Design: 6. Everything is linear if plotted log-log with a fat magic marker. http://spacecraft.ssl.umd.edu/akins_laws.html http://spacecraft.ssl.umd.edu/akins_laws.html

rrobukef 6y ago
No log-log plots nor fat magic markers in this paper though.

rrobukef 6y ago

Wonderful paper! I wonder if amateur real-world simulations are possible based on public data (streets, population density, daily movement). The computing power needed for 100,000 nodes, ~8 edges, ~30-60 sim. days, >>100 experiments seems fairly limited. An estimated 5 GFLOP should be possible for a desktop in reasonable time.

scoot_718 6y ago

Most of the Covid infection curves I've seen are linear because the scales are logarithmic.

derbOac 6y ago

This is a really great paper but I thought there was a general move to network-based models anyway? I recall it coming up during quarantine policy discussions. Nice work though. It seems more practically evident to me now than early on. In my area, the returning growth seems driven by medium sized clusters that are scattered geographically and aren't the same as what you might have thought early on, in that it's not spreading evenly in densely populated areas.

lmilcin 6y ago

I don't think it's true. I believe the reason we have linear or stable infection rates is that the determination to stop the virus grows as the number grow and then wanes as infection rates fall. This basically works like a thermostat (viro-stat?) and is due to governments or large parts of population not willing to put up with restriction when rates are falling ("why do I need to comply, this is no longer a real problem?") This is what I see here in Poland. The government supposedly "closely" watches the situation and puts new restriction wherever the infection rates spike but then promptly removes them when they start falling to what is described as "acceptable level". This is no way to combat the virus, this is the recipe to keep it around indefinitely.

gnusty_gnurc 6y ago

Michael Levitt has been arguing covid-19 never experiences the apocalyptic exponential growth that most people/media seem to think is going on. With a Gompertz curve, we start out with very high growth in the beginning but the growth constantly declines from the outset. Even the idea of network-based analysis and heterogeneity was something he talked about back in March or thereabouts IIRC. https://www.medrxiv.org/content/10.1101/2020.06.26.20140814v2 https://www.medrxiv.org/content/10.1101/2020.06.26.20140814v...