Stochastic Epidemic — Gillespie SSA

Exact stochastic simulation of SIR dynamics using the Gillespie algorithm (SSA). Each event (infection or recovery) is drawn from the exact waiting-time distribution — no time-step approximation. Multiple trajectories show stochastic variability around the mean-field ODE.

S(t)

I(t)

R(t)

Mean-field I(t)

N (population) 1000

β (infection rate) 0.30

γ (recovery rate) 0.10

I₀ (initial infected) 5

Trajectories 5

R₀ = β/γ = —
Peak I: —
Final R: —