Herd Immunity Explorable

What is Herd Immunity?

Herd immunity is refers to the concept the group protection from an infectious disease that emerges when critical mass of the population are immunized from that recieving the disease. In the majority of cases, immunization stems from recieving vaccination against the disease. These immunized people in the community reduce the odds that a disease can spread from person to person. In other words, persons that are not immune to disease can still be shielded against contracting it by virtue of others in the population being unable to pass it on. The greater number of people immune to a disease, the less likely of a chance that someone vulnerable to the disease will contract it. Herd immunity is important because there people who cannot be vaccinated against certain diseases such as those who are too young, too old, or allergic to the vaccination. These people must rely on those around to get vaccinated so that the diease has lower odds of spreading to them.

Calculating Herd Immunity

A population is deemed to have achieved herd immunity against an infectious disease outbreak when they have reached or surpassed the herd immunity threshold, denoted as Q_c. To calculate the value of Q_c, one would need to know the basic reproductive rate of the specific disease, denoted as R₀. R₀ is a numeric measure representing the average number of infections made by that specific disease based on it's various attibutes such as method of spread and duration if infection. The higher that number is, the more infectious the disease is said to be. Using the entire equation, we can determine the herd immunity threshold calculated by solving for the equation Q_c = 1 – (1/R₀).

For example, mumps can have a reproductive number (R₀) of 7, so when we plug it into the equation, it becomes Q_c = 1 - (1/7). Solving the equation gives us 0.86. In other words, 86% of the population needs to be immunized.

However, this calculation makes the assumption that a vaccine against the disease will be 100 percent effective. In reality, vaccines are not perfect. Therefore to find the real world vaccination rate required for herd immunity, we also need to factor in imperfect vaccines by dividing Q_c by the effectiveness of the vaccine(E). Thus, the population required to reach herd immunity threshold can be approximated as V_c = Q_c/E.

In our previous mumps example, the effectiveness of getting two doses of the mumps vaccine is 88 percent. When that number is converted to a decimal, we can get the equation 0.86/0.88 = 0.97, which converts into 97%. In reality, 97% of the population is actually needed to reach herd immunity against mumps! When the vaccination coverage of a population has the necessary percentage for herd immunity, the disease is thought off as "contained".

Your Turn

Watch the effect of vaccination and herd immunity in action by simulating your own outbreak. In the simulation you will be able to modify the reproductive rate of your disease, the effectiveness of the vaccination against it and the vaccination rate of the population. In the simulation, your fictitious disease will have ten attempts infect someone in a population of 250 people. Each time the disease infects a person, it will spread twice according to the reproductive rate you set – once to the R₀ number of closest neighbors from the initial infection, and then again for each of the neighbors infected. To incorporate some real life randomness, the location distribution of the vaccinated, unvaccinated and vaccinated but vulnerable is randomly distributed. This will cause some variation the simulation, but you view see the average results on the line graph.

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