"Opium, what kind of elasticity is it?"

As soon as we finished talking elastisity in class last time, a picture rushed into my head: a increasingly crazy demand for opium in China during the period of Opium War. Before Opium War broke out, China, who received a great amount of profit from exporting silk and tea to other countries, is a highly advanced and fertile country. Unfortunately, China quickly earned envy from other countries, such as British and France. In order to open the great market of China, British began to exported opium to China. From then on, Chinese people fell into a hopeless gulf. More and more people got addictied to opium and became too morbid to protect their homeland when it was invaded. Even thougth the price for opium jumped incredibly, there was no evidence for a decreasing demand for opium. Adversely, as people's addition to opium became serious, more opium is demanded.
I think it may understate the relationship between the price and opium demanded if we simply use the perfect inelastisity. Do we have another type of elasticity that could better describe this special market of opium during that time? Do we have to come up a new elasticity?