Mosquitoes can also carry the AIDS virus. Sleeping sickness is a disease caused by mosquitoes. There are vaccines that prevent the contraction of Malaria and sleeping sickness. There is a cure for Malaria, but it is very expensive and not available to everyone. The Plague of the Middle Ages were carried by rats.
Malaria is highly contagious.
Lyme disease and Rocky Mountain fever are transmitted by ticks. The first was put in use in the 1920's and 30's.