There's a lot of formalism surrounding the study of how much parameters matter; the field is called "dynamical systems" and often covers topics like bifurcation theory and chaos theory.
In this particular system, the parameters matter, but not very much for the particular question the author was asking. The system is well-behaved; it doesn't bifurcate or go chaotic. Tweaking the parameters will change whether the final level of infections is 10% or 90%, but the overall conclusion that "sexual conservatives taking more partners increases total infections" remains valid.
The conclusion isn't valid, IMO, because the assumptions are way off, again IMO. I think the "high-activity players" are at least two orders of magnitude more active than he models them, for example (in a conservative society which frowns deeply on premarital sex). Fewer of them, but more connected; and their numbers will go down, drastically, with more liberal attitudes.
In this particular system, the parameters matter, but not very much for the particular question the author was asking. The system is well-behaved; it doesn't bifurcate or go chaotic. Tweaking the parameters will change whether the final level of infections is 10% or 90%, but the overall conclusion that "sexual conservatives taking more partners increases total infections" remains valid.