Epidemic Spread Simulator (2D)

Outbreak Parameters

Transmission probability 45%

Contact radius 1.0 m

Recovery time 8.0 d

Vaccinated at start 0%

Live Population

Susceptible

Infected

Recovered

Peak infected

Day

0.0

Reproduction R₀

–

SIR Model (live)

dS/dt = 0 people/day

dI/dt = 0 people/day

dR/dt = 0 people/day

Effective Rₜ = –

S / I / R over time

How it works

Each dot is an autonomous agent wandering the arena at random. When an infected (red) agent comes within the contact radius of a susceptible (blue) one, transmission happens with the chosen probability; an infected agent recovers into immunity (green) after the chosen recovery time. Vaccinating a share of the population before the outbreak starts removes them from the susceptible pool from day one — the classic herd-immunity effect.

The panel above reports the standard SIR compartmental model fitted live to the running agent simulation: dS/dt = -βSI/N, dI/dt = βSI/N - γI, dR/dt = γI, where N is the total population, γ = 1/recovery time is the removal rate, and β is the transmission rate backed out each simulated day from the actual number of new infections. The effective reproduction number Rₜ is estimated each day as new infections divided by γ·I (how many people the current infected pool is removing that day) — the same ratio public-health dashboards use in real outbreaks. The basic reproduction number R₀ rescales Rₜ back to a fully susceptible population (R₀ = Rₜ·N/S): above 1, the outbreak grows; below 1, it dies out.

Susceptible Infected Recovered