The characteristic rash of measles is itself an immune response, and is a good marker for progression of the immune response. Patients with immunodeficiency can have a much more limited or even absent rash. In most patients, if it's been 4 days since the appearance of the rash, and they have improvement in fever, runny nose, and conjunctivitis, without a productive cough, they probably aren't infectious. If you have that data (fever and mucous membrane inflammation), I'd pay attention to that as well as the time since the appearance of the rash. A sick patient with measles should be kept in respiratory isolation regardless, but if you're looking at modeling disease transmission, you can follow the symptom progression.
As far as death is concerned, there are several pathways. Measles can cause a poorly understood immunosuppression and immune dysregulation, which certainly contributes. The most common cause of death is pneumonia (often secondary pneumonia), but early diarrhea can be a major cause in malnourished children. Otherwise immunosuppressed individuals (e.g., HIV, and primary immunodeficiencies) can develop a fatal measles encephalitis (a brain infection). Some deaths result from a fatal post-infectious autoimmune syndrome.
Some of these individuals are probably still shedding virus (diarrhea, primary measles pnuemonitis or encephalitis), many of them aren't (secondary pneumonia and autoimmune cases).
Many texts focus on vaccination and the current epidemiology of measles in developed countries, but Cecil Medicine has a very good chapter (375) on the clinical manifestations of measles. There is an interesting article in Lancet Infectious Diseases about the US army outbreak in 1917-18 that is a good example of the interaction of measles with other respiratory pathogens.