I'm not sure I like the term "drug epidemic". An epidemic is, in medical terms, a disease with an infecion rate that exceeds other outbreaks in recent history or prediction models. Drugs do not have an infection rate per se but I understand what you're getting at. I do however feel like the term "drug epidemic" makes the question needlessly loaded. Perhaps "rates of substance dependence" would be an acceptable substitute?

Another definition we would have to handle before the question can be adequately answered is where we draw the line for what a drug is. By far the most common types of substance dependence in the world today are alcohol, tobacco and caffeine. If we include these in the definition then we will have events such as the coffee/tea/tobacco trade routes that greatly affect the rate of substance dependence in the western world. However, if we do not include them, based solely on the fact that they are legal today then we would also have to handle the problem of other substances that were, at the time, legal such as LSD in the early hippie movement or opium in China.

Based on this, would you consider rephrasing the question and clarifying more specifically what you want to ask about with regards to what constitutes a drug?