Measles is a highly infectious disease that is accompanied by symptoms such as a fever, sore throat, and a rash over the body. It is spread through the air via coughing and sneezing. While it is a highly contagious virus, it can easily be prevented through vaccinations. In fact, measles was eliminated from the U.S. in 2000; however, the virus is continually re-introduced from other counties, and regional outbreaks of the disease have since occurred.
In 2014, 2 young men came back from a trip abroad to their Amish community in Knox County, Ohio. While abroad, they were unknowingly exposed to measles, and upon their return they spread the virus to their community members. Due to limited participation in preventative healthcare among Amish communities, these 2 men - along with many of their community members - were not immunized against the measles. What resulted was an outbreak of over 383 confirmed cases of measles in the population of 32,630 from the Amish communities and nearby counties.
Immunizations impact a population by decreasing the number of susceptible individuals. Below shows a graph of infected individuals over time in a population of 1,000 people. How does the rate of immunization affect our sample population? Is there a vaccine rate that appears to successfully control the disease? Play with the slider and click 'vaccinate' to see the impact!
*Please note that this simulation is for learning purposes only and consists of averages and simplifications of real world scenarios. In this example, the rate of transmission for measles was set to 90% and the rate of recovery was set to 14 days.
It takes a 95% vaccination rate for measles to be successfully controlled in a population of a certain size. When enough individuals are vaccinated, the disease won't survive or spread quick enough to cause a substantial outbreak. This is called herd immunity, or the protection of a group from the spread of a certain disease due to having enough of either immunized or recovered individuals from the disease. Since immunizations decrease the amount of susceptible individuals and increases the amount of those immune, even those who have not been vaccinated can still be protected.
The SIR model is used to predict the spread of a disease over time and can also be used to estimate the amount of immunized individuals needed for herd immunity. The model creates a standard equation for the rate of change for susceptible, infected, and recovered (or immune) individuals in a population. Below are the basic SIR equations used to calculate the rate of change of individuals in a population. Note that the rate of transmission is dependent on the external conditions that contribute to the likelihood of becoming infected, such as number of people who come in contact with one another, and the rate of recovery is characteristic of the given disease.
S = Susceptible
I= Infected
R = Recovered
a = rate of transmission
b = rate of recovery
Δ S = -aSI
Δ I = aSI - bI
Δ R = bI
From these equations, we can predict how the disease will spread over time, and help us take action to work towards controlling it. For example, the number of susceptibles can be decrased with vaccinations, and the rate of transmission can be decreased by implementing public health programs (like washing your hands). By knowing the rate the disease spreads, we can start to figure out what the best way to control it is.
Despite being heavily eradicated in the United States, measles may still be present in other countries. Since it is so contagious, it is best to get vaccinated despite an assumption of herd immunity in a community. You especially don't know if someone has been exposed abroad which makes getting a vaccination the only sure way that your chances of being infected, and the chances of those around you getting infected, stay low.