An epidemic is generally a widespread disease that affects many individuals in a population. An epidemic may be restricted to one locale or may even be global (pandemic). An outbreak of a disease is defined as being epidemic, however, not by how many members or what proportion of the population it infects but by how fast it is growing. When each infected individual is infecting more than one other individual, so that the number of infected individuals is growing exponentially, the disease is in an epidemic state. Thus even if the number of people affected is small, the phenomenon may still be called an epidemic, although for small epidemics the term "outbreak" is more often used.
For an epidemic state:
Where R0 is the basic reproduction number of the infection and S is the proportion of the population who are susceptible to the infection. This is merely a mathematical formalisation of the rule stated above.
Some examples of historical epidemics include the Black Death, or bubonic plague, of Mediaeval Europe, the influenza epidemic concurring with the end of World War I, and the current AIDS epidemic.