Wednesday, July 15, 2020

Compound Interest

Compound interest is a miracle.

Consider that in seven cycles at a growth-rate of 1.1 per cycle that the population has doubled.

Conversely, if the growth-rate is negative, say 0.9, then the population is essentially halved.

In twenty-five cycles the population has grown by a factor of almost eleven for the 1.1 while it has diminished to 8% of the original population for the "growth-rate" of 0.9

The numbers for twenty-five cycles for 1.2 and 0.8 are 95X and 0.3% respectively.

Small changes in growth-rate when near 1.0 have enormous, long-term ramifications.

Mortality vs Morbidity
Mortality is the death-rate directly associated with Covid-19. It has been steadily dropping.

Morbidity are the long-term health consequences from having it.

Even though the mortality rate is subject to debate, most reports place it in the neighborhood of 1% +/- 0.7%

The morbidity numbers also have a very wide range but let's use 10% of the mortality rate for an estimate. For the sake of argument, lets assume Covid has serious morbidity rates that vary between 3% and 17% of patients.

How serious?

Covid seems to have an affinity for red blood cells and the carnage they wreak causes clots to form in blood vessels.

The issue presents in many different ways, depending on where the clot "lands" and the tissue that is deprived of oxygen.

If the clot lands in your brain then it is called a stroke. Since 15%-to-20% of your heart's output goes to the brain, 15% of clot-related issues are likely to be a stroke where you lose some brain function.

If the clot lands in your heart it is called a heart attack. Also, potentially very debilitating.

If the clot lands in your kidney, you lose your ability to process some kinds of waste and might require dialysis.

If the clot lands in an artery feeding an extremity, the tissue dies and becomes a potential incubator for gangrene. You could easily lose part of one or more limbs.

Around the internet
Reading around the internet, I see calls to eliminate certain steps that have been taken to remediate the spread of Covid.

Masks are a common example.

Commonly, the writer rails about the fact that masks are too porous to capture virus and they leak.

True. However they capture a significant fraction of the saliva and mucus droplets that contain virus. We do not have a gland that generates purified virus and injects them into our breath as we sneeze. The virus exists in dead, sloughed off cells and in the mucus/saliva that aerosols when we sneeze/cough.

The person who complains is usually visualizing Covid as a single generation of spread. For that kind of analysis a 0-1, binary approach is valid. You either don't get it or you do.

From a community health, epidemiology standpoint thinking of the spread in the community is more like a problem of compound interest.

The current state in Michigan has the virus smoldering. Most people are aware of how common it is in their community. Eaton County (population about 100k) has had 300 confirmed cases and 7 deaths. We have not had a death in about a month-and-a-half.

There are some sub-cultures where the rate is much higher, just as can be said about chlamydia  and syphilis. The benefit of everybody wearing a masks is that when Typhoid Mary sneezes she will only eject 20% of the droplets into the air that she would have sans-mask. And Typhoid Mary WILL NOT wear a mask unless it is required.

That means that you are 80% less likely to inhale one when you enter the store forty minutes later.

So I am going with the flow. I am staying away from crowds. I am wearing a mask at Wally-World. I am washing my hands more. When talking with people, I make a point of standing cross-wind from them so I am not downwind of them and they are not downwind of me.

Not because Big Retch told me to. But because it makes sense when viewed as a "compound interest" problem.


  1. What happens when the mucus and saliva containing virus dries? Does the virus stay entombed in it, or does it become a powder that is then carried away and spread by future breaths?

    1. Great question.

      I don't know.

      I suspect that if the humidity is low it might electrostatically bond to other particles or to surfaces.

      If floating around, it is vulnerable to discharge due to air make-up or vulnerable to filtering.

      In time, UV kills it.

      I cannot give any kind of quantitative answer. Qualitatively, a lower rate of loading means a lower density at equilibrium.