Epidemic Household Clumping Effect

How household structure amplifies transmission beyond mean-field

Household Model

In household epidemic models, within-household contacts are much more frequent than between-household contacts. This clumping causes the effective R₀ to exceed the mean-field prediction.

R₀(household) = Rg + Rh/(1 - SAR) Within-household: SAR = secondary attack rate Between-household: Rg = global contacts × p_infect Effective threshold: R_eff = Rg + n·q·(1-q)^(n-1) (Becker-Dietz formula) n = household size q = within-HH transmission prob

The household structure creates pockets of intense transmission even when the global R is near 1, enabling persistence below the classical threshold.

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