How COVID-19 Spreads Person-to-Person
COVID-19 is a respiratory illness caused by a Novel Coronavirus which is spread when a susceptible person breaths in droplets or aerosols produced by an infected person coughing or sneezing—and for particularly infectious individuals, even breathing—or when the susceptible person touches contaminated surfaces and then touch their mouth, nose or eyes.
For each interaction, the likelihood of transmission from one person to another is increased when a susceptible person interacts with infected persons or environments more frequently, for longer periods of time, and more intensely, through closeness and physical contact. The risk of infection is multiplied by the number of infected people a susceptible person is exposed to.
Every interaction is a roll of the dice. Not every exposure will result in infection, but an increase in each of the factors—frequency, duration, intensity and exposure—increases the odds of transmission.
COVID-19 Infection Timeline
Symptoms for COVID-19 begin about five days after infection. One of the most insidious features of the disease is that it may be infectious two or three days before symptoms start to show, and infected people who never become symptomatic may even be contagious. This means that even those who are cautious about spreading the disease may not know they pose a danger.
In typical cases, symptoms are mild and last about ten days. Critically, infected people appear to remain contagious for about two weeks, although infectiousness is likely at its peak for the few days after symptoms emerge. The course of the illness can be uneven, and it usually takes two or three weeks for the most critical cases to require hospitalization. Hospital stays tend to be long, lasting weeks in some cases.
How COVID-19 Spreads
In an epidemic, R0 (“R-naught”) is the number of people, on average, each contagious person infects. Diseases with R0greater than 1 spread. Currently, COVID-19 has an estimated R0 of 2.3, meaning that on average, each contagious person infects about 2 1/3 susceptible people. “On average” is important—a single contagious individual can infect many more than 2 others, offsetting the care that other contagious people may take to limit their transmissions.
Infections spread through physical social interaction networks, which follow a few basic patterns. We tend to cluster into densely interconnected groups, which are typically relatively small. Families are obvious examples, but we also cluster into personal circles, as well as clusters in workplaces, churches, social organizations, and the like. These relationships tend to be high on the frequency, duration and intensity dimensions, but lower on the exposure dimension because relatively few people are usually in these kinds of clusters.
Second, we form interpersonal relationships across clusters, which create bridging relationships. These relationships are generally lower on the frequency, duration and intensity dimensions, but they much higher in terms of exposure because we generally have many more “weak tie” bridging relationships than close friendships.
Finally, we congregate in lots of different ways, including in workplaces, schools, churches, stores, restaurants, bars, movie theaters, sports arenas, and many other venues. These kinds of interactions vary in terms of frequency, duration, and intensity, but they tend to create tremendous exposure to many other people in a single setting.
If you mash all of these things together, you get a small world network. Small worlds feature lots of interconnected clusters which can be reached in just a few hops. It doesn’t take many wide-ranging bridging relationships to turn large worlds into small ones. (This is, incidentally, what creates the six degrees of separation.)
Small worlds are important in infectious networks because clustering creates many opportunities for an infection to take hold, and bridging ties allow it to spread widely in just a few links. And recall, with R0=2.3, COVID-19 has about two weeks to infect only 2 1/3 other people, at which rate it will spread geometrically. COVID-19 is spreading quickly at a quickly increasing rate, which is what makes it so difficult to predict and manage.
“Super spreaders” has become popular as description for something that can dramatically accelerate the spread of a disease. At least two properties of interaction networks can disproportionately accelerate transmission. One is cluster size. Larger clusters have many more rolls of the dice (interactions) than small clusters, and the risk grows disproportionately to group size. A cluster with 5 people has 10 possible interactions; a cluster with 10 has 45, 4.5 times more with a simple doubling in size. Groups of 20 have 190 possible interactions. This is what makes congregations so dangerous. A high school gym with 1,000 spectators has almost 500,000 possible interactions. While it’s unlikely that every spectator will get within 6 feet of every other spectator, the risk of exposure is still extremely high, and larger events are dramatically worse.
Something else we know about social networks is that not everyone is equally connected. In fact, in most communities, a few people will have many, many more connections than the average person. Extremely social people, those who interact closely with many people, can be super spreaders, especially if they’re super infectious. Cases in China and South Korea have confirmed that one person can infect more than 50 others. In the first network example, just 10 of the 98 people account for a large number of the total interactions, and they act as bridges closing the gap between otherwise distantly connected others. In difficult times, these are the kinds of folks who tend to be the ones others rely on for support—think, for example, pastors—which paradoxically in the case of infectious agents make them especially likely to be vectors for widespread transmissions.
Strategies for Limiting the Spread of COVID-19
The network diagrams we’ve used thus far are highly stylized, useful for demonstrating principles, but not an accurate picture of the size and complexity of real social networks. In fact, accurately diagraming actual social networks of any size is really difficult. They tend to look like a plate of spaghetti.
(average of 10 interactions per person)
And that’s still a dramatic simplification of what a real interaction network looks like. A typical community network would be bigger than the 250 people in the diagram, and it would be much more densely interconnected, so dense that with even the finest lines the diagram would look like a solid disk. Each of the people in the network above has an average of only 10 ties. Think of how many interactions—by which we mean getting within 6’ of another person—you have in a typical day, much less a typical week or two, the time that, on average, a person infected with COVID-19 remains contagious.
Again, each line represents a roll of the dice in a game of chance in which you’re betting that the other person in the interaction isn’t infectious and that, if they are, the infection will not be transmitted to you. In an environment where we don’t know how many people are actually infected, this is a big gamble.
Most epidemiological models assume “random mixing”—every person in the community has equal probability of bumping into every other person. In a small world network, where everyone is two or three links removed from everyone else, this is actually a pretty good approximation. But it breaks down when we start to remove the biggest clusters and the bridging ties. This is good news.
(with limited social interactions)
The social distancing strategy we now have in place in Arkansas turns small worlds into large worlds in which a contagion has to follow a longer path to spread from one cluster to another. The diagram above depicts what a network might look like if congregating events—work, school, church, games, movies—and bridging ties were to be removed. The diagram is an extreme example—in reality the clusters will be still be connected, but sparsely—but it demonstrates the goal of the policies. Each individual is less exposed to others, and it is takes longer for the disease to make its way across a long chain of interactions.
Social distancing is a strategy that works well in the early stages of an epidemic with low infection rates, especially when combined with aggressive testing and contact tracing (tracking down close contacts of infected individuals). It buys time to find out who is infected, and it greatly helps to identify and isolate their contacts.
It is not a great strategy later in an epidemic, after the infection has made its way into the community. By then, it’s likely that the infection will have infected individuals in lots of social clusters, and if so each of the members of a cluster with even one infection is at risk barring strict physical isolation. Because COVID-19 is so stealthy, and because our testing capabilities have been so woefully inadequate, we are not sure how early or late we are in the game.
Shelter in Place policies, which restrict people to their households, are enacted when an infection has spread through a population. This is the ultimate in cluster fragmentation (separation) strategy. Aside from the most essential of essential services, each household is a cluster unto itself. It is, of course, the most successful strategy for containing the infection, but at enormous social and economic cost, and conformity generally requires enforcement that makes people across the political spectrum uneasy.
(Ties only within households)
Ideally, social distancing will be sufficient to slow the spread enough to protect our health care system and our health care workers. Cities and communities in Arkansas—which are much less physically dense than large urban areas—are better situated to avoid the kinds of catastrophic hospital failures seen in New York and Italy, but current projections are that we’ll have to maintain strict social distancing for at least a few weeks to make it work.
End Note
The COVID-19 pandemic has proven vexatious for many reasons that go beyond its novelty, and thus our lack of immunity, and its infectiousness. Because it can be infectious before people begin to show symptoms, and perhaps even transmitted by asymptomatic carriers, it is devilishly hard to manage, especially without adequate testing. That many of its early symptoms mimic those of the common cold, flu, and even allergies, makes the task even harder. Two or more weeks of infectiousness give the virus a long time to spread. The range of intensity of symptoms is very broad—from no symptoms to fatal—and age and a few existing health factors notwithstanding, it is difficult to predict which cases will become critical. Long intensive hospitalizations, a substantial proportion of which require intensive care, add further stress to already strained facility, equipment and pharmaceutical capacity. Pushing back the spread of the disease will buy us the badly needed time we need to meet these challenges.