The disease may be naturally occurring but is most often a manufactured weapon in biological warfare that has been spread by accident. A desperate race may ensue to contain and treat the diseased. The survivors may have natural immunity but frequently have acquired immunity from some government connection, possibly this connection is to the government which unleashed the disease. The survivors rebuild the population while fighting the disease and a second outbreak. Some survivors may interpret the disease as a religious punishment that spared only the just or faithful.
Alien invasion may either decimate the population or destroy the habitability of the Earth. Survivors may fight back in war or attempt to escape the Earth in search of a new home planet. Invasion may also come from a supernatural source, such as zombies, or mutated humans who seek to supplant human culture, I am Legend. The Day of the Triffids is similar except that the invaders are an intelligent and lethal plant life that had been genetically engineered for economic purposes.
Nuclear holocaust was a popular element during the cold war era and the paranoia caused by the space race. This destruction is the result of either direct attack in a war or of misfired weapons. The survivors are understandably hostile and distrusting. Crude clans or governments form according to rule by fist. The threat of nuclear fallout or mutation haunts characters.
Planet of the Apes
A Canticle for Leibowitz
The Book of Eli