Diffusion of Opinion during the Mask-Wearing Debate of Covid-19 Pandemic
From the beginning of the Covid-19 pandemic this year, there have been several measures introduced to contain the disease, including a general recommendation from CDC for wearing masks starting in April 2020. Before this requirement is actually enforced in multiple states, there have been long debates over the usefulness of wearing masks, and each person decides whether to wear a mask based on their own preferences and what they observe from other people. In this blog post, we will try to interpret the diffusion of mask-wearing practices among Cornell students in terms of the threshold model for diffusion.
We start by constructing a diffusion model for this scenario. We will model each student as a node in the network, with the edges created when two students are taking the same class. While there are indeed other public gathering scenarios like club meetings parties, these situations are harder to model since they tend to not have a stable group of participants, so we will omit these cases for simplicity.
In the beginning, the model would have everyone with the opinion that a mask is not necessary, which is the norm before we have the Covid-19 pandemic. During February and March, there were some masks-wearing advocates who begin to wear masks in public (regardless of the general trend), and we will treat them as the initial nodes in the network that has switched toward the alternative option of wearing masks.
In reality, we observe that the initial proportion of people wearing masks in March is oftentimes well below the typical majority choice threshold 1/2. Among all of my Spring 2020 classes, only one out of five of them had almost full mask coverage in March before classes end, and that is also a small class with only 20 students. Since I have other classes with a total number of participants around 480, I need to have a critical probability below 1/25 to switch to wearing masks, and this means I need to have a very strong personal opinion to start wearing masks in my daily life at that point.
We also note that while the decision from the diffusion model analysis above is that most people would not have strong motivations for wearing masks in general, people can make separate choices of mask-wearing based on the different communities that I am in. In particular, if I were in that particular class with more than half of the students already wearing masks, the diffusion model applied to this particular cluster would imply that I should at least wear a mask for the duration of that course. Indeed, this is what I did in practice, and most of my friends followed this as well (it’s just for many of them there are no classes at all that reach the 1/2 threshold).
From the above discussions, we see that the diffusion model gives us a nice way to interpret our personal choices of wearing masks in the early stages of the pandemic where no outside intervention is involved. I think this is a cool insight to have that will also apply to other scenarios, including the debate on vaccination of Covid-19 that just took place very recently.
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