[feral]

I think there's lots of ways to formulate this to see how it's percolation. I'm not a percolation expert though so please call me out if you are, and I'm wrong:

To sketch here:

Consider R the reproductive number of a disease (or R_e, the effective reproductive number, to be specific). This depends on both the inherent contagiousness of the disease, but also on the behavior of the population. If people choose to have fewer contacts (or bars are closed) then R decreases.

Let's say covid is spreading. We ask people to limit their contacts, and see if this stops spread.

We can think of this as trying to remove edges from the contact graph that the disease spreads on.

The contact graph becoming connected or unconnected as we remove edges is clearly percolation.

(Subject to some modeling assumptions about edges being removed at random, but these assumptions are common to both Erdos renyi graph models and SIR style compartmental models).

Make sense?