I did notice in the model that the turtles are getting sick if they run into any other turtle, not just when they run into a sick turtle. To fix this, in the collision with turtle block, add an "if" block around the current code in there that says if color of collidee is red. This will ensure that your turtles only get sick when they encounter a sick turtle.
Vaccination is a lot like getting sick--if the turtles encounter a doctor, how could you change them so that you know they are vaccinated. Maybe color, shape, size? How could you make sure that these vaccinated turtles don't get sick? Like telling the turtles the can only get sick if they run into a red collidee, you could also tell the turtles to only get sick if their color is blue and they are normal, healthy turtles.
It may take some time, but feel free to reply back if you try this and have more questions. Thanks!