Critical Thinking Activity with FRED Models

Experiment #1: What is the impact of R0 on disease spread?

R0 is a measure of the contagiousness of a disease. For R0 of 1, each infected person infects only one other person – the disease spreads but doesn’t spread rapidly.R0 is pronounced R-naught.

For R0 of 2, each infected person infects two people – the disease rapidly spreads. The 2 newly infected people infect 4, those 4 infect 8, and the 8 infect 16. Soon hundreds are being infected.

For R0 of 3, each infected person infects three people – the disease spreads much more rapidly. The 3 newly infected people infect 9, those 9 infect 27, and the 27 infect 81. A disease of R0 = 3 quickly gets out of control.

Fortunately most infectious diseases have R0 between 1 and 2, however for measles R0 = 18!

Below are links to outputs of three FRED models where everything is the same except R0. After clicking each link you will have to download a prevalence video – its safe! You will probably need to look at the output videos a couple of times to answer the following questions:

  • How many days pass until a disease outbreak has infected the maximum number of people?
  • How many days until the disease has completed its outbreak?
  • Which R0 outbreak would be easiest to treat?

R0 = 1.0: FIPS=42003_R0=1.0
R0 = 2.0: FIPS=42003_R0=2.0
R0 = 3.0: FIPS=42003_R0=3.0


R0 Days to Max Infection Days to Outbreak End


What three conclusions can you derive from this table?

Experiment #2: How does herd immunity affect the spread of an infectious disease?

Here is an excellent demonstration of the effect of herd immunity on the spread of an infectious disease. Herd immunity is the protection of the unvaccinated portion of a population because there is smaller chance of unvaccinated people coming in contact with an infected person. Thus, an infectious disease cannot readily spread.

This link provides two FRED simulations of the outbreak of measles in the state and town of your choosing:

Once you select the town, two maps will appear of the county containing that town. Click the black arrow at the bottom left of each map and watch the number of infected people rise and then fall as days pass. Eighty percent of the community depicted in the model results shown in the left map were vaccinated against measles, and 95% were vaccinated in the right map. Watch the spread of measles in these two maps and fill in the tables below:


Location: County: State:
Vaccination Rate Days to Max Infections Days to Outbreak


  1. Was the measles outbreak large, medium or small with 80% vaccination rate?
  2. Was the measles outbreak large, medium or small with 95% vaccination rate?
  3. What would you guess is the vaccination rate needed to insure herd immunity for measles?
  4. What clues do the maps provide about the geographical controls of disease spread?
  5. Are you vaccinated for measles?


Experiment #3: What is the vaccination rate needed to initiate herd immunity?

In Experiment 2 you saw that a high rate of vaccination is needed to cause herd immunity to basically eliminate the spread of measles. In this experiment you will examine a different disease modeled to occur in a town under different levels of immunization/vaccination. R0 and many other things are identical in these models, only the percent of people immunized (Imm; 0.1 = 10%, etc.) being the main term that changes. Based on experimentation with these models what is the immunization rate needed for herd immunity for this disease?