Coronavirus: Social distancing

Do increasingly draconian social distancing measures accomplish anything? Here is one way to look at it.

Let us assume that there is a particular type of exposure, say using a public restroom, and that this is associated with an average probability, p₁ of becoming infected. The probability of not being infected by this exposure is 1-p₁. Assuming that a person's risk of becoming infected with repeated exposures are independent of each other, the probability of not being infected in two exposures is (1-p₁)², and the resulting risk of being infected is 1 minus the probability of not being infected or

P_I=1-(1-p₁)²

For N₁ such exposures, the risk of being infected is

P_I=1-(1-p₁)^N₁

The same reasoning holds true for different types of exposures with different probabilities of transmitting the virus.

For two such exposures the probability of becoming infected is

P_I=1-(1-p₁)^N₁(1-p₂)^N₂

where p₁ is the probability of infection associated with the first exposure, N₁ is the number of the first type of exposures, p₂ is the probability associated with the second type of exposure and N₂ is the number of such exposures.

We can extend this to any number of exposure types. The key point is that different exposure types are associated with different probabilities of transmitting infections. The effectiveness of social distancing depends on its effects in minimizing the Ns associated with the various exposure types. There is much more benefit to decreasing the number of exposures associated with a high risk of transmitting the virus, and less so to those with very low probabilities unless the baseline N of such exposures is extremely high.

The high probability, and thus risk, exposures are those associated with behaviors that have a high risk of inoculating the nasopharynx or oropharynx, such as sharing a drinking glass, or eating something with unwashed hands after touching a contaminated surface. Low risk exposures would be taking a walk in a park. Mid-level exposures would be shopping in a grocery store.

Avoidance of high risk exposures, for the most part do not require official enforcement. Given adequate information, most people would do an effective job of minimizing risk. The more draconian, and often stupid prohibitions, result in diminishing returns, e.g. buying "non-essential items" when also buying essential ones, because they affect very low risk exposures that have minimal effect on the overall risk.

There is no question that there is a benefit to social distancing. However, the heavy lifting is done by common sense, not politicians and bureaucrats with a need to look like they are doing something.