During lockdowns, household bubbling strategies paired households to reduce isolation without accelerating transmission. The intuitive approaches — match by household size, match by age composition — were obvious policy choices. Valdez and Peressutti show that matching by number of working members is better on both axes: comparable epidemic control, but over 40% of the population can participate in social bubbles, far more than size-based or age-based approaches allow.
The reason is that workers are the transmission bottleneck. During a lockdown where only economically active members leave the house, the number of workers determines a household's connectivity to the disease network. A household with zero workers is isolated regardless of bubble assignment. A household with three workers is a hub regardless. The optimal strategy is to pair households that have at most one worker each — minimizing the number of external contacts created by the bubble while maximizing the number of people who benefit from social connection.
Size-based matching misses this because household size and worker count are only loosely correlated. A large household of retirees has zero workers; a two-person household of two employed adults has two. Matching the retirees with another large household achieves nothing epidemiologically and wastes a bubble slot. Matching the two-worker household with a zero-worker household creates one transmission link. Matching two two-worker households creates two.
The result holds across real demographic data from multiple countries, validated by both numerical simulation and generating function analysis of the household contact network. The epidemic risk profiles are comparable across strategies, but the social connectivity — the fraction of the population that gets to interact with someone outside their household — differs dramatically.
The policy implication is that the relevant demographic variable for bubble design was never the one being optimized. Size and age were visible and politically salient. Worker count was the load-bearing parameter.