Herd Immunity & Vaccination Coverage Simulator

Outbreak Controls

Vaccination coverage 40%

Basic reproduction R₀ 3.0

Population 200

Infectious period 7 d

Currently infected

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Ever infected

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Herd immunity threshold

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How it works

Each agent starts susceptible (blue), pre-immune from vaccination (green), or is one of a handful of seed infections (red). Every simulated day, an infected agent has a chance to infect any susceptible agent within contact range; that chance is set by the transmission rate β = R₀·γ, where γ = 1/(infectious period) is the recovery rate. After its infectious period ends, an agent recovers and turns gray, immune from then on. As the immune fraction (vaccinated + recovered) grows, infected agents run out of susceptible neighbors to reach and the outbreak dies out on its own — that tipping point is herd immunity.

β = R₀ · γ,  γ = 1 / infectious period
herd immunity threshold = 1 − 1/R₀
outbreak fades once immune fraction ≥ threshold

Vaccination coverage — the fraction of the population immune before the outbreak begins.
R₀ — how many people one infected agent would infect in a fully susceptible population; higher R₀ raises the herd-immunity bar.
Population — number of agents simulated; larger crowds make the outbreak curve smoother and less noisy.
Infectious period — how many days an agent stays contagious before recovering; longer periods give the disease more chances to spread per case.

Real-world relevance: this is why public health targets a coverage rate above 1 − 1/R₀ for a given disease — measles (R₀ ≈ 15) needs roughly 93% coverage, while a milder seasonal illness (R₀ ≈ 2) needs only about 50%.

Susceptible Infected Recovered Vaccinated

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