Mumps
Mumps is spread from person to person through contact with respiratory secretions, such as saliva from an infected person. When an infected person coughs or sneezes, the droplets aerosolize and can enter the eyes, nose, or mouth of another person. Mumps can also be spread by sharing eating utensils or cups. The virus can also survive on surfaces and then be spread after contact in a similar manner. A person infected with mumps is contagious from approximately seven days before the onset of symptoms until about eight days after symptoms start. The incubation period (time until symptoms begin) can be from 12–25 days, but is typically 16–18 days. 20-40 percent of persons infected with the mumps virus do not show symptoms, so it is possible to be infected and spread the virus without knowing it.
Measles
Measles is extremely infectious and its continued circulation in a community depends on the generation of susceptible hosts by birth of children. In communities that generate insufficient new hosts the disease will die out. This concept was first recognized in measles by Bartlett in 1957, who referred to the minimum number supporting measles as the critical community size (CCS). Analysis of outbreaks in island communities suggested that the CCS for measles is around 250,000. To achieve herd immunity, more than 95% of the community must be vaccinated due to the ease with which measles is transmitted from person to person. The disease was eliminated from the Americas in 2016.