Tuesday, April 7, 2020

Let us handshake some virus proofs

We want to find equilibrium conditions among a population divided between immune and infected, with a ratio of infected to immune.

At equilibrium, the arrival of a virus to a neighborhood will be independent of any other virus invasion. Further the appearances of the immune will e gaussian. We know this beause we have a pit boss, us, who are forcing that balance down to some known error bound. The game, for us, it to find the neighborhood unit size for the reactionary force that specifies the quant.

The hedging of us, the pit boss, means we can treat this as the S/L problem, we have a two color flow. We have two poisson queues, the virus distribution is far left, most neighborhoods at equilibrium will see no outbreak, and almost never do two adjacent neighborhoods see an outbreak. The antibodies can be treated equivalently, but the immune queue size is forty time larger due to immune time to remission time ratios.

So now we see the problem, as a checkout manager problem. Clerks are viruses, coming in at a low, random rate to occupy checkout stands.  The antibody ready for the next virus, and we never run out of checkout counter space. 

We can compute this right off the poisson charts, but we need to pick a neighborhood size. And picking that size is called quantization, and that is the name of the game. Once you have that size, then 1 of 40 of those sizes will see an outbreak. But the neighborhood size can be reduced substantially, that is the thing, get local control forces in action soon reduces the actionable neighborhood size and that keeps the outbreaks very small, local and contained.

Home triage, helps a great deal, the neighborhood size can be reduced to a block with neihborhood watch. Done with small out breaks of a couple of houses, and almost never leaves the block.

But whatever the tolerable level of control we use, the probability drops way down because that poison distribution for antibodies covers the virus sufficiently that the 'almost never spreading to adjacent neighborhoods' is justified. It will look like seasonal flu outbreaks.

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