The game is is all about treating the Patients that come into your Hospital but, like real life, that doesn't always end well and so the game has a death mechanic built in. Curing a large number of patients, or a certain percentage of visitors, is important to the game and is often featured on the level progress screen , with patients deaths counting against you. Your kill and cure counts will appear on the Yearly Appraisal screen.
There are main reasons for patients deaths are the Hospital taking too long to cure them or the player taking a chance on a possible cure. There are two different animations that play when a Patients dies, they either float up slowly into the sky whilst heavenly music plays or the Grim Reaper appears and shoves him into a fiery hole in the floor.
Throughout a patients stay in the hospital they have a face icon (mostly a smiley face) hovering over them as they move around the Hospital. If they get worse, parts of this face will turn into a skull and when the process is finished the patient will die.