Huntington's Disease, sometimes known as Huntington's Chorea, is a severe genetic neurological disorder. It affects people mainly in later life, by which time they could already have passed it on to their children. There is a 50/50 chance of inheriting this disease.
There are many symptoms of this disease, some of which do not surface until later life when the disease has been shown to come into full swing. Firstly there are notable changes in movement i.e. lack of coordination, abnormal bodily movements known as 'chorea' (shaking, jerking). Secondly there are changes in behavior, i.e. mood swings, irritability, increased aggressiveness and sometimes psychosis or dementia.
There is currently no cure for the disease itself, but help can be given to help the sufferer to live a normal life, examples include: medications to control the chorea as well as the mood swings that are key characteristics of the disease.
In House M.D., House orders Thirteen to take the presymptomatic genetic blood test to determine whether or not she has the disease, since her mother had died from it. She objects because she would prefer to not know whether or not she actually has it, the reason being that not knowing gives her the ability to summon up the confidence to do things that she wouldn't normally do. In the episode House's Head, Thirteen starts acting strangely and House quickly gets suspicious. In Wilson's Heart Thirteen takes the test; we see her sitting in a dark laboratory processing her test. The results for the test come out positive for the disease, and Thirteen then crumples up the results and walks away. Whether or not Thirteen actually looked at the results is unknown because the camera doesn't show her looking at them.
In Season Five, Thirteen will have to come to terms that she has this disease. Her fellow colleagues are also aware of her disease in Season Five, and Foreman does tests which reveal she doesn't have as much time left as they thought she did.