Say you had a sample pool:
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
you can see that within the total pool are separate pools and the goal is to turn every 0 into a 1 by the least amount of insertions possible, while each insertion turns the 0's next to it to 1's.
So what you're going to do is, since each 1 turns the 0's on each side of it to 1's as well, you will use the number that is the GCD of both the infection and the pool. in this case 3 is the infection radius and 12 is the pool length so 3 is the GCD, so you would infect every 3rd dose in this case.
I imagine [they] built a model and determined the GCD of the 'pools' they wanted to infect and utilized that number to come up with the amount of tainted doses and distribution.
maths niggers, cuz fuck yeah!