Table 3:

Model parameters estimated by Bayesian inference based on daily deaths until 1 July 2020, assuming that after first lockdown ${\mathcal{R}}_{\text{c}}\left(t\right)$ begins a gradual return to the baseline ${\mathcal{R}}_0$ at a fixed rate (corresponding to T₂ = 120 days in this case). Model selection based on maximum log-likelihood (LL) and Akaike information criterion (AIC). Best fitting models have lower AIC scores (bold). Infection fatality ratio, ϕ = 0.9%. Herd immunity threshold $\left(\mathcal{H}\right)$ calculated from ${\mathcal{R}}_0$ and CV using formulas (14) or (22), as appropriate. T₀ and T₂ parameterise linear reduction and increase in transmissibility, respectively, before and after first lockdown (larger T ⇔ lower slope; Fig. 6).

	Heterogeneous susceptibility		Heterogeneous connectivity		Homogeneous
	Median	95% CI	Median	95% CI	Median	95% CI
Common parameters
c1 a	0.3133	(0.2989, 0.3277)	0.3182	(0.3002, 0.3419)	0.2358	(0.2291, 0.2419)
η b	15	{15}	15	{13, 14, 15}	17	{17}
v c	2.521	(2.369, 2.653)	1.822	(1.681, 2.011)	0	–
England
T 0	−14.79	(−14.991, −13.922)	−14.815	(−14.994, −13.952)	−11.51	(−13.00, −10.17)
${\mathcal{R}}_0$	3.438	(3.380, 3.470)	3.451	(3.383, 3.533)	3.017	(2.940, 3.109)
$\mathcal{H}$	15.46%	(14.06%, 17.15%)	14.97%	(12.55%, 17.29%)	66.85%	(65.99%, 67.84%)
Scotland
T 0	−2.253	(−3.033, −2.010)	−2.229	(−2.930, −2.007)	−4.407	(−5.651, −4.017)
${\mathcal{R}}_0$	3.308	(3.263, 3.358)	3.319	(3.268, 3.388)	3.234	(3.194, 3.302)
$\mathcal{H}$	15.01%	(13.68%, 16.74%)	14.53%	(12.22%, 16.77%)	69.08%	(68.69%, 69.71%)
Model selection
LL	−951.7		−960.5		−3308
AIC	1917		1935		6627

^atransmissibility reduction due to lockdown 1,

^bdifference between mean-time-to-death and mean-time-to-recovery (sampled from a continuous interval and reduced to the nearest integer before entering the model),

^ccoefficient of variation (CV).