Network analysis of England's single parent household COVID-19 control policy impact: a proof-of-concept study

Lockdowns have been a core infection control measure in many countries during the coronavirus disease 2019 (COVID-19) pandemic. In England's first lockdown, children of single parent households (SPHs) were permitted to move between parental homes. By the second lockdown, SPH support bubbles between households were also permitted, enabling larger within-household networks. We investigated the combined impact of these approaches on household transmission dynamics, to inform policymaking for control and support mechanisms in a respiratory pandemic context. This network modelling study applied percolation theory to a base model of SPHs constructed using population survey estimates of SPH family size. To explore putative impact, varying estimates were applied regarding extent of bubbling and proportion of different-parentage within SPHs (DSPHs) (in which children do not share both the same parents). Results indicate that the formation of giant components (in which COVID-19 household transmission accelerates) are more contingent on DSPHs than on formation of bubbles between SPHs, and that bubbling with another SPH will accelerate giant component formation where one or both are DSPHs. Public health guidance should include supportive measures that mitigate the increased transmission risk afforded by support bubbling among DSPHs. Future network, mathematical and epidemiological studies should examine both independent and combined impact of policies.