Household Bubbling Strategies for Epidemic Control and Social Connectivity

Abstract

During the COVID-19 crisis, policymakers have implemented "social bubble" merging strategies, which allowed people from different households to meet and interact. Although these measures can mitigate the negative effects of extreme isolation, they also introduce additional contacts that may facilitate disease spread. As a result, several modeling studies have explored the epidemiological impact of different household-merging strategies, in which the selection of households to be merged is guided by specific demographic criteria, such as household size or the age composition of their members. Here we investigate an alternative pairing strategy in which households are merged according to the number of economically active (working) members. We develop a mathematical model of household networks using real demographic data from multiple regions around the world, and simulate a lockdown scenario in which only economically active individuals can leave their households, while the remaining non-working members stay indoors. By using numerical simulations and the generating function technique, we then estimate the epidemic risk for different household merging strategies. We found that merging strategies based on the number of working members can keep epidemic risk at similar levels as those based on household size. Moreover, the worker-based approach allows significantly more people to form larger social bubbles, exceeding 40\% of the population in some countries. We found that merging households with at most one worker provides the best balance between controlling epidemic risk and addressing people's need for social contact.

Figures (5)

• Figure 1: Panel a) In the main figure, we show the household size distribution $P(s)$ for Argentina, and in the inset, we display the same curve but on a log-linear scale. Panel b) Probability of having $w$ workers in households of size $s$ (ranging from $s=1$ to $s=12$) in Argentina.
• Figure 2: Schematic figure showing how two households (cliques) are merged into a single bubble. Circles represent non-workers without external contacts, and squares represent workers with external contacts. Black links indicate internal household connections, while blue links indicate external connections. On the left, a household of three members with one worker ($s=3$, $w=1$) and a household of four members with one worker ($s=4$, $w=1$) are shown separately. On the right, the two households are combined into a single bubble with seven members and two workers ($s=7$, $w=2$).
• Figure 3: Fraction of recovered people $R$ at the final stage in the $\beta^I-\beta^E$ plane for homogeneous (panel a) and heterogeneous (panel b) external connections. Simulation results were averaged over 1000 stochastic realizations on networks with $N=5\times 10^5$ individuals. To compute $R$, we exclude those realizations without epidemic outbreaks ($R < 0.5$%.). The dashed line shows the analytical prediction from Eq. (\ref{['eq.betaEcbetaIapprox0']}) ($\beta^I\approx 0$), while the solid line corresponds to the critical threshold at $\beta^I=1$ from Eq. (\ref{['eqBetaEc']}).
• Figure 4: Results for the household merging strategy "$w^*=1$" in Argentina. Panel a: household size distribution $P(s)$ before merging (black) and after merging (red). The inset shows the same distributions in log-linear scales. Panel b: Scatter-plot of the fraction of recovered people $R$ at the final stage as a function of $\beta^E$ for $\beta^I=1$. Black circles correspond to the case without household merging, while blue circles correspond to the merging scenario $w^*=1$. Panel c: Heatmap of the final fraction of recovered people in the $\beta^I-\beta^E$ plane, restricted to realizations in which epidemics occur. The white dashed line shows the analytical approximation of the critical curve for $\beta^I\approx 0$ and for the household merging strategy "$w^*=1$". This line was obtained from Eq. (\ref{['eq.betaEcbetaIapprox0']}). Similarly, the solid line indicates the critical value $\beta^E_c$ for $\beta^I$ after the merging strategy is applied. For comparison, the red dotted lines correspond to the critical curves without household merging shown in Fig. \ref{['fig.NoMerg']}a.
• Figure 5: Results for the remaining household merging strategies. Panel a: scatter-plot of the fraction of recovered individuals $R$ at the final stage as a function of $\beta^E$ (with $\beta^I=1$) for all merging strategies, including the case without merging. Panels b-d: Heatmaps of the final fraction of recovered individuals in the $\beta^I-\beta^E$ plane, for the following merging strategies: $w^*=2$ (panel b), $w^*=w$ (panel c), and $1+s$ (panel d). The white dashed lines show the analytical approximation of the critical curve for $\beta^I\approx 0$. These lines were obtained from Eq. (\ref{['eq.betaEcbetaIapprox0']}). Similarly, the solid lines indicate the critical value $\beta^E_c$ for $\beta^I$ after the merging strategy is applied. For comparison, the red dotted lines correspond to the critical curves without household merging shown in Fig. \ref{['fig.NoMerg']}a.