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Back of the envelope #Probability for why active countermeasures needed on #coronavirus.
If disease spreads by Galton-Watson process --- each sick infects random number (maybe 0) other ppl.
What's probability the disease dies out on its own?
If disease spreads by Galton-Watson process --- each sick infects random number (maybe 0) other ppl.
What's probability the disease dies out on its own?
Prop 10.6: supercritical GW has >0 probability of never dying out!
super-critical means R0 > 1
For #COVID19 estimates of R0 all over the map, but all are >> 1.
Example
super-critical means R0 > 1
For #COVID19 estimates of R0 all over the map, but all are >> 1.
Example
What's Prob( dies on its own ), i.e., let nature take its course and it will "just disappear" as @realDonaldTrump is hoping?
Theorem 10.4: Solve for the fixed point phi(t) = t, where phi(t) is generating function of offspring distribution.
Theorem 10.4: Solve for the fixed point phi(t) = t, where phi(t) is generating function of offspring distribution.
Some scenarios:
R0 = 2.14 (approx = maximum likelihood from above paper)
Prob( dies out ) = 23%
R0 = 2.14 (approx = maximum likelihood from above paper)
Prob( dies out ) = 23%
R0 = 3.08 (with max infection of 9 people)
**very realistic** given current data
Prob( dies out ) = 8% (still only assuming a finite upper bound on spreading)
Only gets worse when account for possibility that 1 person spreads to 10, 100, 1000 people.
**very realistic** given current data
Prob( dies out ) = 8% (still only assuming a finite upper bound on spreading)
Only gets worse when account for possibility that 1 person spreads to 10, 100, 1000 people.
For comparison: Flu has of 1918 had R0 of about 1.8 -- see how that turned out
Calculation isn't prediction of what *will* happen but what *could* happen under basic dynamics without any outside intervention to stop.
For the "evidence-based" crowd: all evidence points to R0 >>> 1
===> super-critical behavior
===> non-zero (HIGH) probability that COVID19 continues indefinitely
===> super-critical behavior
===> non-zero (HIGH) probability that COVID19 continues indefinitely
Definitely not GW long term. But possible not a bad approximation at the very early stages when effective population much larger than number of infected.
A good starting point for heuristics and explains why serious efforts to stop spread needed EARLY when R0 > 2
A good starting point for heuristics and explains why serious efforts to stop spread needed EARLY when R0 > 2
Compare to heuristic of the Nudge Bros: “it hasn’t killed enough people yet”
