3 Viruses Go "Viral"

Activity 2

How Contagious Is it?


The purpose of the activity is to introduce students to the mathematical construct R0 that predicts the number of people who can contract an infectious disease from one infected individual (secondary infections), and, therefore, is a measure of contagiousness of a disease under certain conditions. Students learn about the uses of R0 and its limitations in predicting the course of an epidemic. They compare the R0 values of different viruses and consider the basis for the differences in infectivity.

Students then use a second mathematical equation to determine the percentage of a population that needs to receive the measles vaccine in order to prevent an epidemic. Students then read about the concept of community or herd immunity.

In a mock town meeting students take sides as to whether the Department of Public Health in their city should enforce a stricter vaccination policy that would require all children to be vaccinated against childhood infectious diseases. Students, either as a team for vaccination or against vaccinations prepare to present and discuss the role of vaccination in disease prevention, an analysis of the arguments for and against vaccination using evidence from the literature and the ethical issues surrounding vaccinations.


  1. Randomly assign students the role of being either for or against a stricter vaccination policy.
  2. Individually, have students read the introduction to the activity and sections about R0. Encourage students to watch the video that explains R0.
  3. Before having them address the task, conduct a discussion about the possible reasons the R0 values may differ from virus to virus, the value of knowing R0 of a virus, and its limitations.
  4. After the students have completed their calculations to determine the percentage of the population required to prevent a measles epidemic, have them view the interactive that demonstrates the difference in the spread of measles when the population is 80% vaccinated vs. 95% vaccinated and compare their findings to that of the interactive.
  5. Have students read about community immunity and discuss how the interactive map relates to that concept. Students should understand that the map demonstrates that when 95% of the population is vaccinated, most (but not all) of the 5% unvaccinated individuals are protected from infection. When only 80% are vaccinated protection through community immunity does not happen.
  6. Students should prepare notes on
    • the role of vaccination in preventing measles outbreaks;
    • their calculation of the percentage of the population that needs to be vaccinated to prevent a measles outbreak in the community, including an explanation of how this number was determined;
    • a discussion of how vaccinating a certain percentage of the population can prevent outbreaks and epidemics;
    • their analysis of the pros and cons of vaccination, including evidence for and against arguments on both sides;
    • their conclusions as to whether vaccination for all children should be required including justification of their conclusion using evidence from the literature.
    • a discussion of the possible of ethical implications of requiring vaccination and of not vaccinating a child.

Students then work in two teams, one to prepare a presentation in favor of a stricter vaccination policy and another against a stricter vaccination policy. Remind students that they will participate in a discussion after the presentations. A vote will be held at the end of the discussion. Remind them also that they should feel free to change their minds regardless of which team they were on.

Short readings are provided to initiate student thinking and writing. Students should be encouraged to seek further information about these topics using valid sources. Remind them that they need to cite their sources in their reports. You may want students to present the highlights of their reports in a discussion or in a poster.

Links to Background Readings:

When should you worry about getting sick from your best friend and when can you feel it’s okay to hang out together even when she is feeling pretty crummy? You have already determined that if your friend is sick from food poisoning, you cannot catch that from her, unless, of course, you finish her half eaten lunch. But what if your friend has measles? Or Ebola?

During the recent Ebola and measles epidemics people in the United States were terrified of contracting Ebola but very unconcerned about measles. However, the likelihood of contracting measles from your friend is far greater than that of catching Ebola.

Several factors determine contagiousness of an infectious disease. One factor is how the infectious agent is transmitted. Transmission of Ebola requires very close contact with bodily fluids whereas measles is transmitted through the air in virus-laden droplets that can travel a distance and remain on objects waiting to be transferred by touch to someone’s nose or mouth. Other factors include:

  • how many virus particles are present in the droplet or body fluid,
  • how long an individual remains infectious (that is, how long the infected person is producing virus),
  • and the numbers of individuals in the vicinity of the infected person who are susceptible to infection.

Taking into account these factors, infectious diseases can be given a basic reproduction number, termed R0, that indicates the average number of individuals (secondary infections) who can be infected by a single infected person in a susceptible population. That is, R0 means the number of new cases generated by a single existing case.

Reproduction by the Numbers - R0

Table 1 shows the R0 values for several viruses.

Disease Transmission Mode R0
Measles Airborne Droplet 12-18
Mumps Airborne Droplet 5-7
Rubella Airborne Droplet 5-7
Smallpox Airborne Droplet 5-7
AIDS Sexual Contact 5-7
SARS Airborne Droplet 2-5
Influenza Airborne Droplet 2-3
Ebola Bodily Fluids 1.5-2.5

The Value of Knowing R0

Knowing the R0 of an infection can help determine whether a disease might spread through a population. If R0 is less than 1 (R00 is equal to 1 (R0 =1), the disease will remain in the population but will not escalate to an outbreak or epidemic. If R0 is greater than 1 (R0 > 1), the disease will spread and an outbreak or epidemic is possible. The higher the R0 value the more contagious the disease.

For instance, measles with an R0 of 18 means that a single person infected with measles can infect 18 other unvaccinated or never before infected individuals whereas Ebola with an R0 of 2 can only infect two susceptible people. The following video explains this idea further:

The Limitations of R0

Although knowing R0 of an infectious agent can be useful, it is not an absolute number. No population is homogeneous (that is, all the same) in its susceptibility to an infectious disease. Some individuals may have been vaccinated; others may have had the disease before and are therefore immune. Still others may never have contact with an infected person.

However, knowing the R0 of a virus can provide an indication of how many people in a population need to be vaccinated to ensure that an outbreak or epidemic does not occur. In other words, what percentage of a population needs to be vaccinated in order to bring the R0 value of an infectious agent equal to 1 where the disease is stable and will not spread?

A rule of thumb is the higher the R0 value, the higher the percentage of the population that must be vaccinated in order to keep the infection from spreading.

In the following scenario you determine the percentage of the population that must be vaccinated to prevent a measles epidemic.

Measles Outbreak in California Spurs Call for Vaccinations

The recent measles outbreak at Disneyland has had departments of health around the country rethinking their vaccination policies.

In past years, vaccination against several childhood diseases including measles, mumps and rubella were required before students could enroll in school.

More recently, however, increasing numbers of parents are requesting exemptions to this requirement based on religious or personal beliefs or on unfounded fears about the side effects of vaccinations.

Your Task

In light of the recent outbreaks of measles your city has decided to return to a stricter enforcement of the vaccination policy requiring that all children receive vaccines against childhood infectious diseases. However, not everyone in the city agrees with this idea. A town meeting will be held to hear citizens concerns on both sides.

Your teacher will randomly assign every student as either as being supportive of required vaccinations or against required vaccinations. Individually you will prepare notes on the specific topics listed below and then get together with your group (pro or con) to prepare a presentation and select a spokesperson.

Every student should be prepared to contribute to an open discussion following the presentations and to vote on whether vaccinations should be required, and what exemptions, if any, should be allowed.

Topics to include in a presentation:

  1. The role of vaccination in preventing outbreaks or epidemics of contagious diseases
  2. Finding about the percentage of the population that needs to be vaccinated to prevent a measles outbreak in your community. Include an explanation of how you reached this number
  3. A discussion of either the pros or cons of vaccinations including evidence for arguments on your side. Include references for the sources you use.
  4. Your conclusion as to whether vaccination for all children should be required. Be sure to justify your conclusion with evidence from the literature. Cite your sources.

Your first step is to determine the percentage of the population that must be vaccinated in order to prevent an outbreak in your city. Following this, you need to take notes about the role of vaccination in infectious diseases. As part of this you will need to identify the concerns and arguments as to why vaccinations are important or why they need not be required. You will need to find evidence upon which arguments for and against vaccinations are based. It is important to consider both sides of the issue in order to defend your stand You will also need to consider the concerns involved in requiring vaccinations and in not vaccinating a child.


To calculate the percentage of the population that must be vaccinated you need to know the following:

  • Assume the R0 of measles is 18
  • The goal is to have the R0 = 1 in order to prevent the spread
  • The equation for determining the percentage of the population needed to be vaccinated is:
goal R0|current R0
percentage of population to vaccinate in order to stop the spread

Watch the following video to understand this equation better:

The following interactive map demonstrates the difference in spread of measles depending on the percentage of the population vaccinated in a city in Pennsylvania. How does your calculation compare to this one? Be prepared to discuss the difference in the two maps and why the spread of infection is different.


After viewing the interactive map, read the following background on community (herd) immunity. Think about how the concept of community immunity relates to the interactive map of measles spread.

Community Immunity ("Herd Immunity")

Vaccines can prevent outbreaks of disease and save lives. When a critical portion of a community is immunized against a contagious disease, most members of the community are protected against that disease because there is little opportunity for an outbreak. Even those who are not eligible for certain vaccines—such as infants, pregnant women, or immunocompromised individuals—get some protection because the spread of contagious disease is contained. This is known as "community immunity."

View the slideshow below to see how different levels of immunization can affect a community.



A community in which no one is immunized and an outbreak occurs.


Here, some of the population is immunized but not enough to confer community immunity.


Here, a critical portion of the population is immunized, protecting most community members.

The principle of community immunity applies to control of a variety of contagious diseases, including influenza, measles, mumps, rotavirus, and pneumococcal disease.

Prepare your presentation and select a spokesperson

Be sure you include all the topics listed above and are prepared as individuals to defend your side of the question – should vaccinations for childhood diseases be required of all children in your city?

During the presentations

Listen carefully to the opposing team’s presentation and to all the discussion that follows. After the presentations and discussion, you will vote as to whether a stricter vaccination policy should be implemented. You should feel free to change your mind about the policy no matter which team you were on if you are convinced by the opposing ideas.

Your teacher may provide you with readings on the following topics or you may be required to research them on your own.

  • The role of vaccinations
  • Pros and cons of vaccines
  • Key ethical issues related to vaccines

If you are provided with the readings you should augment them with information from valid sources you find on the web or in the library. Remember, just because you read it somewhere on the Web does not mean it is scientifically accurate or reliable.