Actually cough which lasts less than 2-3 weeks is not a disease.
It is a common reflex action that clears the throat of mucus or foreign irritants. Coughing to clear the throat is typically an infrequent action, although a number of conditions can cause more frequent bouts of coughing.
In general, a cough that lasts for less than three weeks is an acute cough.
A cough that lasts between 3 and 8 weeks, improving by the end of that period, is a subacute cough.
A persistent cough that lasts more than eight weeks is a chronic cough.
Most cough episodes will clear up, or at least significantly improve, within two weeks. If you cough up blood or have a “barking” cough, talk to your doctor. Any cough that hasn’t improved after a few weeks may be serious, and you should see a doctor.