Fig. 4: Criterion for inclusion of household structure for accurate predictions.
Empirical rule of thumb specifying the level of SAR above which a household structure is necessary for output predictions within a 5% relative accuracy for the household structure of a Great Britain (fraction of children = 22.73%, mean household size χ = 2.35) and b Sierra Leone (fraction of children = 53.81%, mean household size χ = 5.85), both with UK-like contact patterns and assortative mixing (though of little relevance, as the same rule of thumb also applies for random mixing: see Supplementary Discussion, Section 2.4). For each R0, data points represent the values of the SAR along the borders between the light blue and red regions in Fig. 3b (more precisely, the values of the SAR at each point of the 5% relative error contour lines, which are not explicitly drawn here to reduce clutter, but are shown as think black lines in Supplementary Fig. 16B) for ϕ = 1, 1.5 and 2 and ψ ranging from 1 to 4. Black data points give SAR values associated with more moderate and realistic differences in susceptibility and infectivity between adults and children (ψϕ ≤ 3) and are typically less widespread than grey data points, which correspond to extreme and unrealistic differences (ψϕ > 3). Regression lines (dashed) fit corresponding-colour data points, excluding R0 = 1.1 and 4, where a linear fit looks unreasonable. The thick black line shows the empirical rule of thumb, with parameters reported in the figure (η1, regression coefficient; η0, intercept), and is empirically chosen to: be closer to the dark than the grey dashed line, reflecting low confidence in extreme differences between adults and children; and provide an acceptable fit for both the SAR values obtained assuming UK-like mixing (here) and random mixing (see Supplementary Discussion, Section 2.4). Note that part of the spread in the data points is owing to the ruggedness of the borders between regions (contour lines in Supplementary Fig. 16B): a smaller step in paa and ψ would reduce the spread but increase the computational cost.
