Madeline says that they can’t study at her house because her brother has measles.
Measles is a highly contagious viral infection causing fever, cough, runny nose, inflamed eyes, and a red rash. It can be fatal. Madeline must be vaccinated against the disease or she would have it herself, and the household should have been quarantined so that Madeline shouldn’t be (and possibly isn’t) living at home while her brother is infectious.
Measles were declared to be eliminated in the US in 2000 by public health officials (this doesn’t mean nobody got measles that year, just that there were so few cases and such high vaccination rates that they weren’t any threat to the general population).
Madeline’s brother getting measles in 2001 is highly unusual, and it really makes you wonder why vaccination rates are so low in the Gilmore Girls universe – in real life, Connecticut has one of the highest rates of child vaccination in the world. It seems more in line with California, where Gilmore Girls is filmed, where vaccination rates tend to be lower.