Table 1:

Model parameters estimated by Bayesian inference based on daily deaths until 1 February 2021 (with reduced models). 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. 2).

	Heterogeneous susceptibility		Heterogeneous connectivity		Homogeneous
	Median	95% CI	Median	95% CI	Median	95% CI
Common parameters
c1 a	0.2968	(0.2958, 0.2988)	0.2993	(0.2976, 0.3015)	0.2751	(0.2740, 0.2772)
c2 b	0.5761	(0.5731, 0.5843)	0.6601	(0.6535, 0.6661)	0.4803	(0.4776, 0.4869)
η c	12	{12}	12	{12}	9	{9, 10}
v d	1.475	(1.470, 1.487)	1.120	(1.111, 1.145)	0	–
England
T 0	3.616	(3.480, 3.759)	0.6549	(0.3925, 0.8821)	7.595	(6.955, 7.771)
T 2	283.5	(282.4, 286.0)	302.2	(295.8, 303.9)	416.1	(408.9, 418.3)
${\mathcal{R}}_0$	2.709	(2.701, 2.716)	2.807	(2.781, 2.827)	2.691	(2.683, 2.701)
$\mathcal{H}$	26.94%	(26.62%, 27.10%)	25.48%	(24.61%, 25.89%)	62.84%	(62.72%, 62.98%)
Scotland
T 0	10.10	(9.854, 10.72)	6.934	(6.460, 7.508)	11.78	(11.36, 12.58)
T 2	360.8	(359.0, 364.4)	399.9	(390.2, 406.3)	540.0	(524.9, 546.9)
${\mathcal{R}}_0$	2.874	(2.856, 2.912)	2.981	(2.948, 3.053)	2.978	(2.954, 2.995)
$\mathcal{H}$	28.29%	(27.88%, 28.69%)	26.75%	(25.81%, 27.52%)	66.41%	(66.14%, 66.61%)
Model selection
LL	−3707		−3684		−5893
AIC	7434		7387		11805

^atransmissibility reduction due to lockdown 1,

^btransmissibility reduction due to lockdowns 2 and 3,

^cdifference 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),

^dcoefficient of variation (CV).