Herd Immunity Simulation (v0.9)

Background Information

This simulator shows you how herd immunity works from a mathematical point of view. We make several assumptions:

• The population is closed. No new people come in or leave the population. It remains steady at whatever number you choose.
• Meetings of people (when dots cross each other) are completely at random. We know this is not the case in the real world. We congregate with people who are like us, people we work with, people we go to school with, or people who ride public transportation with us. Those congregations and "touch points" may not be at random. (In fact, many are not.)
• The percent vaccinated remains what you picked. Often times, people who are not vaccinated will get vaccinated during an outbreak.
• The R-naught (R₀, which is the number of people one case infects) remains the same throughout the outbreak. This is often not the case, as intervention measures can and do change how many people a case may infect.
• The "Infection to Infectious Time" remains constant, and the "Infectious Period" is the same for everyone. This is often not the case. The times from exposure to infection, infection to disease, and disease to recovery vary from person to person. These times depend on many factors like the pathogenicity and virulence of the strain, the infected person's immune response, and their general health.

Instructions

Choose from the value options in the boxes below, and then click on "Start Simulation". The simulation will begin, and you will see a timer below the simulation telling you how much time has passed since the outbreak started.

The simulation will end after two incubation periods without any cases (red dots). This is often how we declare epidemics to be over.

Take Note!

Note the differences in the number of cases, the attack rates between vaccinated and unvaccinated, etc. Pay attention to the histogram of cases (aka "Epi Curve") at the bottom once the simulation ends.

Pay attention to the vaccine effectiveness and percent vaccinated, and go above or below the Herd Immunity Threshold, whose value depends on the R₀ value:

Notice how different the number of cases in the vaccinated and unvaccinated are, depending on the value of "Percent Vaccinated" versus the threshold. And notice the speed at which the outbreak happens.

Common R₀ Values for Diseases

• Seasonal Flu: 2
• Ebola: 2.5
• Diphtheria: 2 to 4
• Common Cold: 3
• COVID-19 (Delta): 5 to 8
• Mumps: 7
• Chickenpox: 10 to 12
• Measles: 12 to 18

Start Simulation

Vaccinated and/or Immune Vaccinated and Non-Immune Unvaccinated Infected

Epidemic Curve