By a huge coincidence, I have a copy of "Running Free" to hand, a biography of Coe from the early 1980s.
Coe's 400m PB was 46.85 in 1979 (age 21), three days before he set the mile world record. He did a relay leg in 45.9 in 1981 as well. His bests aged 19 and 20 were 49.1 and 47.7, so his progression was rapid, but from 19 to 21, you'd expect a rapid improvement. Old Man Coe highlighted early on in Coe's careere that he needed to be able to sprint to sprint to prosper at 800m, so there was a lot of emphasis on speed in training. Plyometrics played a large part in this, as did 200m repeats and 400m races.
By an even huger coincidence, an old work mate of mine had Toxoplasmosis at the same time as Coe and they ended up being treated by the same specialist. Coe's illness was either genuine, or an exceptionally elaborate scam!