Pandemic: The Board Game

An Outbreak occurs when a city that has 3 disease cubes on it already is drawn from the infection deck, adding a "4th" cube. Instead of adding the 4th cube, every city connected to the outbreaking city gets a disease cube instead.

My best recommendation for winning without an Outbreak would be to play on an easy difficult setting (3 Epidemic cards for example) and prioritize treating cubes from cities that have 3. On an easy setting, you have plenty of time to prevent outbreaks in between Epidemics.