The researchers failed to take into account the number of radiant servants of pelor and hunters of the dead constantly curtailing the population.
Apart from that, though, vampries don't produce spawn by one bite. According to Dracula, someone becomes a vampire by drinking the blood of the vampire over a period of days. Even in D&D, a single drain attack won't kill a victim.
Now, the wight situation is different. A vampire spawn doesn't create vampires. Thus, anyone killed by their slam attack rises some time later as a wight. And wights create spawn in 1d4 stupid rounds. So if a vampire kills a few people in a major town, it's going to be Dawn of the Dead a few days later.