Disease Spread and Vaccination
Watch a disease spread through 1000 people shown as 400 dots, and see how vaccination stops it. Choose how many others each case infects (R0), how many days people stay infectious, how many people are vaccinated and how many are infected on day 0. The dots turn from blue to red as the infection spreads outward from the first cases, then to green as people recover and become immune, while vaccinated people carry a ring and are never infected. A graph follows the share of people who are not yet infected, infected and recovered, and a gauge marks the herd immunity level, 1 - 1/R0 (for instance 1 - 1/3 = 66.7 % when R0 is 3), above which the disease can no longer spread. The results give the peak share infected and the day it happens, the total who catch it and how long the outbreak lasts.
Preview — sign up free to change the numbers yourself
What you can adjust
- People each case infects (R0)
- 0.5 – 8
- Days a person is infectious
- 2 – 20 days
- Vaccinated
- 0 – 95 %
- People infected at the start
- 1 – 20 people
How many other people one infectious person infects, on average, while everyone around them can still catch it. Below 1 the disease dies out by itself; the higher it is, the faster and wider it spreads.
How long someone can pass the disease on before they recover. A longer period makes the outbreak slower and longer for the same R0.
The share of people who are vaccinated before the outbreak starts. In this model a vaccinated person cannot catch or pass on the disease. The gauge marks the herd immunity level, 1 − 1/R0, where the disease can no longer spread.
How many of the 1000 people are infectious on day 0. More of them means the outbreak takes off sooner but it does not change how far it spreads.
About this simulation
What it shows
400 dots stand for 1000 people: blue not yet infected, red infected, green recovered and immune, ringed vaccinated. A graph follows each group day by day, and a gauge marks the herd immunity level.
The key idea
While nobody is immune, each case infects R0 others on average. Once more than 1 − 1/R0 of people are vaccinated, each case infects fewer than one other and the disease fades, protecting those who cannot be vaccinated. Measles is roughly 12 to 18, seasonal flu roughly 1.3.
Try this
Run the defaults: 301 people (30.1 %) are infected at the peak on day 23. Set Vaccinated to 40 and the peak falls to 7.24 %. Set it to 70, above the 66.7 % level, and no outbreak starts.
A simple model: everyone mixes evenly, a vaccinated person cannot catch or pass on the disease, and recovering gives lasting immunity. Nobody is born, dies or travels, and the numbers are averages, so a real outbreak would be bumpier. The dots only illustrate the numbers. The days go by faster than real time, and the picture says which day it is.