A famine is an extreme shortage of food, caused by drought, crop failure, disaster, or overpopulation. Famines are often characterized by starvation, and by emigration or exodus (leaving the affected area) to find food.
Famine is simply caused by a countries (or whatever scale you are referring to: city, state, etc...) not having enough food to supply its population... that can be cause my a disease infecting (and...
In Ireland the last great famine started in 1845 and ended in 1852. Worldwide there are several severe famines currently ongoing, many of them a lot worse than the Irish famine.