Epidemic Wavefront

Reaction-diffusion SIR model on a 2D grid. Susceptible (blue) cells become Infected (red) via contact; Infected cells Recover (grey) over time.

Epidemic Parameters

Transmission β 0.30

Recovery γ 0.08

Diffusivity D 0.20

Speed 5×

3.75

R₀ = β/γ · epidemic will spread

Initial Conditions

Controls

Population

Susceptible

Infected

Recovered

Susceptible

100%

Infected

0.0%

Recovered

Steps

SIR equations:
dS/dt = −β·S·I
dI/dt = β·S·I − γ·I + D·∇²I
dR/dt = γ·I

R₀ = β/γ: epidemic spreads if R₀ > 1.
Herd immunity threshold: 1 − 1/R₀.

Epidemic Wavefront Growing