Use graph theory to plan a COVID-19 safe Thanksgiving
It’s OK be skeptical of the experts. Epidemiologists have been struggling to complete their understanding of COVID-19, it is indeed a “novel” coronavirus so as with all things new, the knowledge of it evolves. Regardless of what we have learned (and are still learning) about transmissibility, therapeutics and immunity, we can dispel some of the confusion around how the risks are modeled and scratch our skeptical itches by learning a little about one of the theoretical underpinnings of epidemiology: graph theory. When I say “a little” I mean, bear with me for about 10 minutes.
The rage lately on Twitter, Facebook, Nextdoor and so forth about limiting Thanksgiving this year is heightened. We are all tired of having our social worlds narrowed by COVID-19. Many of us have suffered several months of not hugging loved ones, of not shaking hands, of not enjoying live music events in-person and so forth. We want our schools to safely open, we want to have face to face contact, we want to travel. The increased social pressure of isolation and economic pressure of reduced income are stresses have become new normals we don’t want. We all want a return to the old normal. We would really like to have a COVID-19 safe Thanksgiving.
We can make some decisions about the risks of Thanksgiving travel and gatherings with a little graph theory. Yes, it’s a mathematical concept but even if math usually makes you panic, you don’t need to panic now; the essence of graph theory is easy to understand. Graph theory is used to model many financial and various technical phenomenon. Long before social media had demonstrated “viral” phenomenon, actual viruses demonstrated behaviors that can be modeled with graph theory.
This is how graph theory is applicable to assessing the Thanksgiving risk: We are all “nodes” (or “vertices”) in a large graph of humanity. Every social proximity contact we have is an “edge” that connects nodes in that graph. Those edges each have attributes such as the probability that a contact was infected (localized data is often available from county health department websites), which if any of the nodes (both parties of the contact) were masked (covering nose and mouth), what was the volume of their exhales (were they breathing heavy?), what was the air circulation around them and how close were the contacts.
Now watch this video and re-read the paragraph above.
The National Institute of Health provides some basis:
Whereas in epidemiology, we speak of ‘hosts’ and ‘contacts’, the social literature is based upon ‘actors’ and ‘relations’, while graph theory uses the terms ‘nodes’ and ‘edges’. In each case, however, it is the presence of a relationship between individuals in a population that is the issue of concern. The range of available vocabularies can hinder the transfer of ideas between these fields. We shall refer to ‘individuals’ and their ‘contacts’; the set of contacts of an individual is their ‘neighbourhood’ and the size of this neighbourhood is the individual’s ‘degree’. (source: Networks and epidemic models)
Here at the tail end of November 2020 there is much to be hopeful about on the horizon: therapeutics are being approved, effective vaccines are likely to be available on a limited basis next month and accurate testing, so scarce six months ago, is now widely available. Given what we know now, herd immunity may be established, through a combination of vaccine administration and continued spread of infection, by the summer of 2021. In the meantime, the continued spread of infection is the part we must be wary of as risks are transitive: you personally may not be in a population vulnerable to serious COVID-19 symptoms but your risk of asymptomatically becoming infected and transmitting it to someone who is vulnerable remains high. We should all be alarmed by the case and death rate ramping up leading into Thanksgiving week as we’re not starting it from a low level of infection and death. Here’s some charts from the prior month(source: JHU data on KFF site) —
Note that hospitalizations and deaths are trailing indicators, cases lead by a few weeks but but already deaths have been climbing precipitously.
Now that we’re armed with a theoretical model around contagion, we have some hope on the horizon and we understand where we are from a starting point as far as the nature of the “nodes” in our midst we can have rational conversation about safety if you’re considering traveling and gathering for Thanksgiving. Ask yourselves these questions:
How many different households and geographies would people be traveling from if they were to join for a Thanksgiving gathering? The more people in a gathering, the more nodes in our graph. The more households and geographies, the greater the number of edges.
Of the people joining for a Thanksgiving gathering, how many edges are connected to them and what are characteristics of those edges? Have they been sheltering in place, wearing masks and social distancing or have they been lax about COVID-19 transmission reduction measures? Are their kids in face-to-face school? Are they in a job with high public contact (e.g. working with customers at super-markets)? Each of these are attributes of our edges, cumulatively they amount to a risk level.
We should all plan our Thanksgiving (and other holidays) with these among our considerations (perhaps also include: can you gather for Thanksgiving with attendees spread out? can you gather outside? can you gather with air-purifiers circulating and filtering air?). Canada had their Thanksgiving holiday a month ago, their infection rate has more than doubled and that’s with very light travel reported.
Canada has gone from diagnosing more than 2,000 cases per day in mid-October to an average of 4,776 cases daily in the past week. Few Canadians fly to grandma’s house for a turkey dinner, so the spike there could offer just a taste of the pain Americans could see. (source: Will the U.S. heed Canada’s Thanksgiving lesson?)
For 2020, it’s better to have a virtual Thanksgiving than a ICU Christmas and a New Year’s funeral. Plan on 2021 having a much more joyful and socially connected holiday season but in the meantime, stay safe.
