When both the contagious and the susceptible person wear 50% effective masks, the first mask cuts disease transmission in half, and the second mask cuts it in half again. So disease transmission is 50% × 50% = 25% (compared to when neither wear masks), which means the drop in disease transmission is 75%.
If you think about it, it's surprising that 50% effective masks can reduce disease transmission by 75%. This is possible because when both people wear masks, disease transmission is halved twice. This double protection makes masks much more effective than you might intuitively expect.
Here are all four interactions by which a contagious respiratory disease can spread from one person to another.
So far, we've only considered disease transmission between two people. How do we go from here to understanding disease transmission in the community?
Well, in the extreme limits, this is straightforward.
For example, what if no one wore a mask?
What if everyone wore a mask?
When everyone wears a mask (or when no one wears one), we can calculate the drop in disease transmission in the community, because there's only one type of interaction involved.
But in reality, some people wear masks and others don’t. Which means the virus can spread through a mix of all four interactions.
So how does the likelihood of each type of interaction depend on the mask usage? To find out, take a look at the simulation below.
This simulation shows how often each type of interaction occurs in a crowd of people who are interacting with each other at random. Although the exact percentage of each interaction changes from moment to moment, can you identify any patterns or trends?
The simulation above shows us how the percentage of interactions depends on mask usage. However, because this simulation shows the exact number of interactions at a given time, these percentages can change from moment to moment, i.e. they can fluctuate.
We can solve this problem by averaging the numbers of interactions. The simulation below shows the average percentage of interactions of each type instead of the moment-to-moment percentages. By averaging the data, we can smooth out the fluctuations and identify the trends more clearly.
Drag the slider below to see how disease transmission in a community depends on mask usage. Do these average percentages line up with what you expect based on the previous simulation?