What is the SIR model in epidemiology?

The SIR model divides a population into three compartments: Susceptible (can catch the disease), Infected (currently infectious), and Recovered (immune). Differential equations describe the flow between compartments, allowing epidemiologists to predict outbreak dynamics, peak infection counts, and final epidemic size.

What is R₀ and why does it matter?

R₀ (basic reproduction number) is the average number of people infected by one case in a fully susceptible population. If R₀ > 1, the outbreak grows; if R₀ < 1, it dies out. COVID-19 had R₀ ≈ 2–3 for the original strain. Reducing R₀ below 1 through vaccination or social distancing ends an epidemic.

What is herd immunity?

Herd immunity occurs when enough of a population is immune (through vaccination or recovery) that disease transmission declines and eventually stops, even protecting unimmunized individuals. The herd immunity threshold is 1 − 1/R₀. For R₀ = 2, you need 50% immune; for R₀ = 10 (measles), 90% immune.

How does social distancing affect epidemic spread?

Social distancing reduces contact rates between individuals, effectively lowering the transmission parameter β and thus R₀. In this simulation, the distancing slider slows particle movement, reducing collision frequency. Even modest reductions in contact rate significantly flatten the epidemic curve and reduce peak infected count.

Home▸Medicine & Biophysics▸SIR Epidemic Model - Infectious Disease Spread and Herd Immunity Simulator

🧪 SIR Epidemic Model - Infectious Disease Spread and Herd Immunity Simulator

Explore the SIR compartmental model for infectious disease spread. Adjust R0, recovery rate, and vaccination coverage to observe epidemic curves, herd immunity thresholds, and peak infection timing.

Medicine & Biophysics2DModerate60 FPS

⚙ Under the hood

This simulation demonstrates the SIR model of infectious disease spread, illustrating how susceptible, infected, and recovered populations interact to determine the dynamics of an epidemic. It explores concepts like herd immunity and the impact of vaccination rates.

SIR ModelHerd Immunity

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install