Explanation:

An epidemic is a widespread occurrence of an infectious disease in a population at a particular time. The diseases cholera (option 1), malaria (option 2), and smallpox (option 3), are all capable of becoming epidemics if not controlled. These diseases can spread quickly among a population, either through direct contact, contaminated water or food, or through the bite of an infected mosquito.

On the other hand, Elephantiasis (option 4) is a disease caused by parasitic worms, commonly transmitted through infected mosquitoes. While it can affect many people in a region, it does not spread directly from person to person. Its occurrence is rather based on exposure to the mosquito vector, thus, it is not classified as an epidemic disease, but an endemic one. Endemic diseases are constantly present in a population, but do not rapidly or directly spread among individuals in the same way epidemic diseases do. This makes the correct answer `Elephantiasis`.