Epidemic Household Model — Secondary Attack Rate

Within-household transmission dynamics and SAR estimation

n = 4
β = 0.30
γ = 0.20
N = 20

Household Epidemic Model

The Secondary Attack Rate (SAR) is the probability that a susceptible household member is infected given one index case. In a household of size n with 1 initial case, the final size Z follows:

SAR = E[Z−1]/(n−1) where P(Z=k) via Reed-Frost chain binomial

Within-household R₀ᴴ = β(n−1)/γ. When R₀ᴴ > 1, epidemics regularly infect most of the household. The Reed-Frost model gives: P(escape infection | k infectious) = (1−p)^k where p = 1−e^(−β/γ).