Virus Spread — SIR Model

SIR Compartmental Model

The SIR model divides the population into three compartments: Susceptible, Infectious, and Recovered (immune). The ODEs governing transmission are:

dS/dt = −β·S·I/N
dI/dt = β·S·I/N − γ·I
dR/dt = γ·I

The basic reproduction number R₀ = β/γ determines epidemic outcome: if R₀ > 1, the epidemic grows; if R₀ < 1, it dies out. The peak infection occurs when S = γ·N/β. The final epidemic size satisfies the implicit equation: r = 1 − e^(−R₀·r)