Once in a math congress someone presented a paper on a mathematical model used to predict the impact of certain measures that could be taken in order to control some pest/plague. A guy in the audience interrupted the speaker and asked why not to "kill them all"(referring to the specimens of the pest/plague) and put a stop to the problem. The speaker observed that we were thinking that kind of things because almost all of us were mathematicians and so we were not aware that it would be a big problem to do that.
From my point of view, he was suggesting that "the right way to control a plague is not to kill them all" is a standard, uncontroversial fact that all biologists would agree. My question is about this last point.
Is that a scientific thesis or an ideological one? I mean, do biologists have theories that allow them to know that the "right" way to control a plague is not to kill every specimen of the species?
Why is it the case that we can assure that exterminating a species is necessarily going to affect, directly or not, humankind?
Is it a matter of chance and, as we are not completely certain of what may happen after exterminating the species, then we don't want to take a risk?
Thanks! And feel free to edit tags :)