Wednesday, March 25, 2020

The Okie in Isolation: Disease Modeling

The Okie in Isolation: Disease Modeling
By Bobby Neal Winters

Another beautiful day has dawned. I’ve made it successfully to Wednesday of Spring break.  My day consists of getting up; stretching; showering; breakfast; doing my languages on Duolingo; and then my email.  While I have been instructed to get some rest during this period--and I am as having an electronic wall between me and everyone else reduces stress--the emails do come through because the university is still working.  We are working in isolation, but we are working.
The emails trickle into my inbox, and the rate is small, but if I don’t take care of them they will turn into a lake by the time next Monday rolls around.
For entertainment while I work, I turn to YouTube.  It provides some soothing background noise.  An interesting video that came out today was on Flattening the Curve by Numberphile. They discuss the SIR mathematical model of disease transmission.  The SIR is an acronym where S stands for the number susceptible, I stands for the number infected, and R stands for the number recovered.  Recovered is something of a euphemism because it includes the number of the dead.  The mathematics of this only cares about those who aren’t capable of getting it again. A special case can be modeled by the equations below:

N = S + I + R.
Geeks like me know what those fractions on the left are.  The rest of you should think of them as rates of change with time. On the right side, we’ve thrown in the Greek letters beta and gamma to assert our superiority over you.  It is like when chimps toss poop, but not requiring soap to wash with afterwards.  
The first equation says that the number of susceptible individuals will decrease as more people get it; you’ll either gain immunity or die. So beta is how quick you succumb.
The second equation says that the rate of infection will increase as a higher proportion of the population gets it, but once you’ve got it you're no longer at risk of getting it. (Oh boy!)
The third equation says that the rate of the number recovering is proportional to the number who have it.  So gamma is how fast you get well/die.
The number beta is what we are fiddling with by urging people to stay at home.  The folks on Numberphile have this animated and explain it in more detail for those of you who are interested.
So stay home and decrease beta.

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