2 ms·
>After a day or so of thinking about it and seeing my projection match what was being reported, I concluded China chose this function because it shows a concern
by DoctorOetker 7y ago
>After a day or so of thinking about it and seeing my projection match what was being reported, I concluded China chose this function because it shows a concern but does not cause great alarm. A predictable upward linear growth. Unsettling, but not terrifying.
Initially the expansion was clearly exponential as evidenced by the clean straight line in the log-linear plots.
Under high mixing conditions (like a high N-dimensional cube) this is to be expected for the initial breakout.
Then quarantine and lock-down measures came, and experts expected the second derivative of the cumulative infections to reach a constant, which subsequently happened.
I witnessed a lot of people not understanding 1) why a simple quadratic? 2) why is a quadratic any better??
When there social distance measures are in effect, the virus can only diffuse on territory, and not "teleport" by public transport etc.
This means that it can only spread in 2 dimensions.
Consider the oversimplification of an epicenter, with a disklike area of infection, then a constant radial ground speed through diffusion, would mean the infected area would increase quadratically with radius. And the radius would increase proportionally to time (effective ground speed, since 2 months from now people will not be able to suddenly sneeze 2 times as far...).
So the cumulative number of infections would hence increase quadratically with time.
If we knew the eventual infection percentage (which Gabriel Leung estimated as potentially being 60%?), then we could calculate the effective radial ground speed:
If P is the number of people per area A then rho = P / A is the population density.
If only a susceptible fraction S can get infected and assuming a circular disk, with A = pi R ^ 2 = pi v ^ 2 t^ 2
Then we can calculate the cumulative number of infected people N as N = rho * A * S = rho * S * pi * v ^ 2 * t ^ 2
so the daily new cases would be
dN / dt = rho * S * pi * v ^ 2 * ( 2 * t )
and its slope X would be:
X = d ^ 2 N / dt ^ 2 = rho * S * pi * v ^2 * 2
(units: confirmations per day, per day or confirmations per day ^ 2)
solving for ground speed:
v = sqrt( X / ( rho * S * pi * 2 ) )
Sadly I can not read Chinese for your link, can you fluently read Chinese or did you use something like google translate?