Possible tinfoil but here goes: What if you wanted a certain predictable kill rate from the shot? The only way to get solid data is to test the kill shot on a broad sample of the population and observe the results. Mixing the kill shots with placebo shots spreads the deaths out enough so most will not notice them.

Once you know the kill shot produces predictable results, roll out the mandatory boosters that the sheep must take to work, buy food, get medical care, even go outdoors. The booster will contain the percent of kill shot for the death rate desired.

If you were to release a bio weapon with a 10 percent kill rate, the sheep would trample each other getting in line for a booster