Table 1:

R₀ values for the multi-group host-vector transmission model. As described in the text, the groups differ in terms of the mosquito biting rate (a) and the duration of human infection (ρ), with different levels and directions of correlation between the two heterogeneities (r_aρ). The “Numerical (exact)” column gives (exact) numerical results obtained from a 1000 group model, with group attributes sampled from a bivariate distribution with relative biting attractivenesses of the groups given by a gamma distribution with mean 1 and standard deviation 0.985 (Cooper et al., 2019) and durations of human infection lognormally distributed with mean 290 days and standard deviation 116 days. Other parameters are given in the text and lead to a value of $R_0^{\text{hom}}$ of 23.63. MVN and MVLN formulae refer to results obtained using analytical formulae (eqns 17 and 18), either using means and coefficients of variation obtained from the set of attributes in the 1000 group model, or by using the corresponding quantities from the underlying continuous distribution from which group attributes are sampled. Monte Carlo refers to results obtained using numerically estimated product moments of the underlying continuous distribution from which group attributes are sampled. Monte Carlo estimates were obtained by averaging over 4000 sets of results for the 1000 group model. Both the standard error (quoted as ± value) of this estimate and the standard deviation across the 4000 sets of results (value in parentheses) are given. The standard error, which describes the uncertainty in the Monte Carlo estimate, is obtained by dividing the standard deviation by $\sqrt{4000}$. The standard deviation describes the dispersion of R₀ values obtained from single realizations of the 1000 group model about the underlying mean.

ra,ρ	Sample			Underlying Distribution
	Numerical (Exact)	MVN formula	MVLN formula	Monte Carlo	MVN formula	MVLN formula
0.8	75.89	65.56	84.17	73.58 ±0.12 (7.54)	61.48	80.58
0.5	54.62	50.66	58.54	62.90 ± 0.09 (5.81)	55.89	66.74
0.0	49.15	48.47	49.14	46.60 ± 0.06 (3.56)	46.58	46.58
−0.5	38.15	45.27	35.49	32.49 ± 0.03 (1.88)	37.26	30.03