Hello!
"Epidemic" is the word that is commonly used to describe a new, suddenly increasing disease. However, the term "outbreak" is also often used. These terms are both used to describe a disease that is rapidly increasing or threatens to increase.
Sudden diseases may also result in a quarantine. This means that a certain section of a building, town, state, etc. restricts people from traveling in and out. Quarantines are used to prevent the disease from spreading further and harming more people.
I hope this helps you!