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. 2016 Aug;13(121):20160288. doi: 10.1098/rsif.2016.0288

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© 2016 The Authors.

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

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Figure 3. — The factor by which estimators based on homogeneous mixing overestimate key epidemiological variables in a population structured by households. The basic reproduction number R₀ for Markov SIR epidemics with expected infectious period equal to 1 (a,d), critical vaccination coverage v_c for Markov SIR epidemics (b,e) and v_c for Reed–Frost epidemics (c,f), as a function of the relative influence of within-household transmission, in a population partitioned into households. For (a–c), the household size distribution is taken from a 2003 health survey in Nigeria [29] and is given by for m_i is the fraction of the households with size i. For (d–f), the Swedish household size distribution in 2013 taken from [30] is used and is given by . The global infectivity is chosen, so that the epidemic growth rate α is kept constant while the within-household transmission varies. Homogeneous mixing corresponds to , in which case . Note that the order of the graphs is different in (b) and (e) from that in (a,c,d,f).

Inline graphic — The factor by which estimators based on homogeneous mixing overestimate key epidemiological variables in a population structured by households. The basic reproduction number R₀ for Markov SIR epidemics with expected infectious period equal to 1 (a,d), critical vaccination coverage v_c for Markov SIR epidemics (b,e) and v_c for Reed–Frost epidemics (c,f), as a function of the relative influence of within-household transmission, in a population partitioned into households. For (a–c), the household size distribution is taken from a 2003 health survey in Nigeria [29] and is given by for m_i is the fraction of the households with size i. For (d–f), the Swedish household size distribution in 2013 taken from [30] is used and is given by . The global infectivity is chosen, so that the epidemic growth rate α is kept constant while the within-household transmission varies. Homogeneous mixing corresponds to , in which case . Note that the order of the graphs is different in (b) and (e) from that in (a,c,d,f).