American Sociological Association

Section on Methodology

A publication of the American Sociological AssociationASA News & Events
May/June 2020

Modeling the Impact of Collective Action on Coronavirus Containment (Methodology)

Tim F. Liao, University of Illinois at Urbana-Champaign

Sociologists study how individual choices impact population behavior, sometimes in counterintuitive ways; they also study how government interventions influence individual and collective behavior. The current intervention of physical distancing (also known as social distancing, see Mejívar, Foster & Brand 2020) is a case in point. Physical distancing is being practiced to a varying degree in many countries globally during the current COVID-19 pandemic. Its definition varies from simply keeping a 6-foot/2-meter physical distance from one another to a broad range of measures. Its goal is to reduce the effect of the basic reproduction number, R0, the expected number of secondary infected persons due to one primary infected person in a population with equal susceptibility to a specific disease. 

The new, effective reproduction number, R, is expressed as follows (Becker 2015):

     R=[1-(1-)f] R0  

where R0 is the basic reproduction number, f is the proportion of the population engaged in physical distancing to decrease their interpersonal contacts to an a fraction of their normal contacts, and R is the new effective reproduction number. When a=f=0, the fraction to be infected equals  and this quantity also defines herd immunity. Thus, physical distancing is measured here as a, the proportion of social contacts kept, and f, the proportion of the population engaged in physical distancing, a form of collective action.

Using the formula above, we ran model-generated R values based on the three levels of R0 of 2.5, 3.0, and 3.5 (see the figure in the references). A recent meta-analysis of COVID-19 R0 estimates based on Chinese data reported an R0 range of 1.40 to 6.49, with a mean of 3.28, a median of 2.79, and an IQR of 1.16 (Liu et al 2020). Another study of Italian data suggested a COVID-19 R0 range of 2.76 to 3.25 (Remuzzi & Remuzzi 2020). Therefore, we chose an R0 value of 3.0, an approximate mid-point value for either of the two studies just cited, and a low (2.5) and a high (3.5) value which give a range close to the IQR cited above (Liu et al 2020). The chosen R0 values of 2.5, 3.0, and 3.5 are also used in a recent COVID-19 simulation study (Hellewell et al 2020).

Let us focus first on the model in which R0 is 3.0, a value most probable for the current pandemic (Liu et al 2020; Remuzzi & Remuzzi 2020). It is particularly informative to focus on the values of a and f at which R=1. If R<1, an infectious disease will die out; at any point above R=1, it will spread. In this model, we learn that to reach R=1, we must have 70% of a population (forming a critical mass for collective action) practicing physical distancing by keeping no more than 20% of their old social contacts. When the physical distancing population increases to 80%, they can keep up to no more than 40% of their old social contacts, and when 90% of the population is engaged in physical distancing, they can keep no more than 50%. The difference between the lower R0 (2.5) and the higher R0 (3.5) is about 10% difference in collective action as the 60% curve in the lower R0 and the 70% curve in the higher R0 scenario are comparable.

How does this translate into practice in the current pandemic? When Spain already had 430 confirmed cases, hundreds of thousands of people marched across the country on International Women’s Day. Italy started its lockdown on March 10, but in less than two weeks’ time its interior ministry reported over 92,000 people and 2,000 plus businesses violating restrictions (Euronews 2020). By the Friday before St. Patrick’s Day (March 15), the U.S. already had 2,183 confirmed cases, people still packed bars in all major cities that Saturday night, ignoring physical distancing (The Atlantic 2020). The collective inaction in physical distancing in the three countries contributed to their top positions in terms of the number of positive cases. 

It appears that collective action (f) is more consequential than individual physical distancing (a) (see references). There are three ways to achieve collective action—using selective incentives, internalizing externalities, and creating better knowledge (Liao 1994). Imposing fines for violating lockdown rules is a negative incentive, currently practiced by several countries. To shift the burdens of obeying physical distancing to individuals (to internalize externalities), a government can rely on a multi-level administrative structure for enforcing lockdown down to the neighborhood level, a strategy used by various Chinese cities from January to March. Having a correct and thorough understanding of the importance of physical distancing will enhance collective action. This comment will contribute, we hope, toward that goal.