Some literary critics, like Susan Zieger, have described vampirism as being analogous to addiction (see "Best of the Web" for a link to Zieger's book). After all, vampires could be said to be "addicted" to blood – they might not want to feed on human blood, but they're physically compelled to do so. (Hey, even Edward Cullen Twilight's "vegetarian" vampire relates his desire for blood to an addiction.) Addiction was a hot topic in late-nineteenth-century Britain – it had only recently been defined as a physical condition. Before, doctors used to see symptoms of withdrawal from patients who had been taking laudanum (a mixture of opium and alcohol) for headaches, and simply prescribed more laudanum. It was only in the late 1800s that medical experts put two and two together and realized that it was the laudanum itself that caused the withdrawal symptoms. Considering Stoker's interest in keeping everything about Dracula very contemporary and up-to-date, reading it as an allegory about addiction seems pretty plausible.
Casual opium use for the treatment of nerves, insomnia, and headaches forms the backdrop of Dracula, suggesting that drug use and addiction is an appropriate lens through which we can understand vampirism.
In Dracula, Stoker registers a common British anxiety about the sources of drug addiction: as a foreign immigrant to Britain, Dracula brings with him a highly contagious addiction – vampirism – that threatens to sweep the nation.