Epidemic spread: how much immunity breaks the chain?
Year 12 Biology · a generic pathogen, well-mixed population, mean infectious period 4 days, one index case · you set R0; the model measures Re = R0 × S/N as the susceptible pool shrinks
Set the outbreak
the threshold marker moves when you change R0
0.5cases per case, fully susceptible8.0
0%threshold 1 − 1/R0 = 75%100%
Population
seed 20260831 · run 0
The population
400 of 2 000 shown
Susceptible Infectious, thick ring Immune or recovered
Nothing has run yet.
Live numbers
EFFECTIVE REPRODUCTION NUMBER
1.60above 1: chains grow
R0 set4.00
Susceptible S/N40.0%
Threshold 1 − 1/R075.0%
Day0
Infectious now1
Ever infected1
Final size—
S, I and R over time
Re = 1 where S/N = 1/R0
Susceptible Infectious Recovered or immune where Re = 1
Many outbreaks, same settings
nothing run yet
Press Run 200 outbreaks. The model is stochastic, so the same settings give a different answer every time and only the whole distribution is a claim about them. Batches add up until you change a setting.
Died out early—
Mean of those that took off—
Never infected in those runs—
Ready. Nothing has run yet. Set the two sliders, then run one outbreak — and then run 200, because one outbreak is a single draw from a distribution and cannot settle anything on its own.
Predict first. R0 = 4 and 60% of the population are already immune. Will the outbreak grow or shrink?
Ready. Population 2 000, 60% immune, R0 4.0, so Re starts at 1.60. One index case. Nothing has run yet.