Algorithm 0

A formula

On March 16, the COVID-19 pandemic exploded in Europe. Looking at the worldometer on that day, and kind of remembering when it started, and having picked a credible reproduction number from the internet, he came up with an extremely simple design for a mechanism to naively compute the number of infected people I at moment t:

I_{t} = L_{t} + N_{t} * C

Here are the elements important for running the formula in plain language:

The elements of the formula

# of infected at the end of period t
# in last period, L_{t} is equal to I_{t-1}
# in last-but-one Lb1_{t}=I_{t-2}
# newly infected during last period is L_{t}-Lb1_{t}
repronumber (the mean number an infected person contaminates)
mean length of a period/generation in days (set to 5 days)
the number of periods considered (set to 17)
date of the first contamination, set to December 29, 2019

The Algorithm in Pseudocode

Setup initial values (parameters)
   set I 1 set L 0 set N 0
   set C 2 set g 5 
Setup help variables
  set t 0 set seed-date 0 set day 0
  set n 17 set ticks 0 
a: Process the current generation
   if ticks > n [stop] 
   print [day ticks I]
   set Lb1 L 
   set L I 
   set I  I + (L - Lb1)*C
   set day day + g
   set ticks ticks + 1
   back to a:   
A screenshot produced by algorithm 0


Both the algorithm and the formula must be wrong when confronted with observations in the real world. It does not, for instance, take important phenomena serious. What about how many people are Susceptible and how many Resistant (or dead)? These two (out of the three from the most successful epidemic model, the SIR model, are simply not there. Moreover, changes in the repro-number (for instance induced by ratio, panic or regulatory action) and changes in the contamination times and death rates are not part of the model. Only the number of infections can be found in algorithm-0. So why bother with it at all? The main reason for mr. Sum, who has the lead here, is that the ICg model (the infections (I) as function of a repronumber (C) and a generation period (g)) may be adequate during the time when an epidemic emerges in the world, when we do not yet know much about it, but very soon get an impression about how contageous the virus is and how quickly it spreads — and regulatory measures will have to be contemplated. Look here for further deliberations.


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