## Thursday, March 19, 2020

### Interesting Article On Mathematics Of Community Transmission

I ran into an interesting paper on community-based analysis of the COVID-19 virus by Alexander F. Siegenfeld and Yaneer Bar-Yam*. Since I assume that at least some of my readers enjoy looking at mathematical models, this paper may be of interest.

The following is a verbal summary of the mathematics at the beginning of the paper:
Many studies of disease spread consider individuals as the primary unit of analysis, with the reproductive number—i.e. the number of people to whom an infected individual will on average transmit the disease—playing a central role. It is well known that an outbreak can be stopped if interventions reduce this reproductive number to less than 1.

Here, we consider the spread of disease among communities, mediated by its spread among individuals. Central to our analysis is the analogous community-to-community reproductive number R∗ [1, 2], i.e. the expected/average number of other communities to which a single infected community will transmit the infection. Our analysis makes no assumptions regarding the size of a community; a community could be as large as a country or as small as a city, so long as disease transmission within communities is far more frequent than disease transmission between communities.
The mathematics confirms the common sense reaction: shut down travel, and you want to impose measures to slow down transmission within a "community" (e.g., city or state or province) as quickly as possible, so as to slow down transmission within that community as well. (I do not want to be dragged into controversy discussing other regions, but I would argue that Canadian politicians have probably done as good a job following a similar script as could be expected. Hindsight tells us that a faster reaction would have been better, but I see no evidence that policymakers had enough reliable data to have moved much faster. Historians may be able to adjudicate that matter later.)

In North America, in addition to the shortage of medical supplies, there is a lack of testing capacity. (Other regions are in better shape, others worse.) However, once testing capacity cranks up, we will hopefully be in a position to flood the vicinity of a cluster with tests, and clamp down hard on transmission rates. (The issue is not testing people who have symptoms, rather pin down the carriers with symptoms, and have them quarantined.) The hope is to get ahead of this thing, so that we can create that excess testing capacity.

Obviously, a more permanent solution is vaccination, but I have no idea about the delivery time. (Go, scientists!)

Footnote:

* Alexander F. Siegenfeld and Yaneer Bar-Yam, Working paper eliminating COVID-19: A community-based analysis, New England Complex Systems Institute (March 19, 2020).

(c) Brian Romanchuk 2020