Table 4.

Model parameters estimated by Bayesian inference with transmission constrained by a government stringency index (Hale et al., 2020). Model selection based on maximum log-likelihood (LL) and Akaike information criterion (AIC). Best fitting models have lower AIC scores (bold). Infection fatality ratio, $\varphi =0.9\%$. Herd immunity threshold ($\mathcal{H}$) calculated from ${\mathcal{R}}_0$ and CV using formulas (14) or (22), as appropriate. w accounts for increases in transmission since the end of lockdown 1 due to factors other than government response.

	Heterogeneous susceptibility		Heterogeneous connectivity		Homogeneous
	Median	$95\%$ CI	Median	$95\%$ CI	Median	$95\%$ CI
Common parameters
$c_1$a	$0.2808$	$(0.2806,0.2814)$	$0.2626$	$(0.2624,0.2634)$	$0.2345$	$(0.2343,0.2346)$
$\eta$b	17	$\{17\}$	16	$\{16\}$	16	$\{16\}$
$\nu$c	$1.314$	$(1.309,1.320)$	$0.8298$	$(0.8272,0.8447)$	0	–
England
w	$2.430$	$(2.427,2.434)$	$2.339$	$(2.338,2.345)$	$2.096$	$(2.094,2.096)$
${\mathcal{R}}_0$	$2.336$	$(2.334,2.337)$	$2.398$	$(2.398,2.400)$	$2.356$	$(2.354,2.358)$
$\mathcal{H}$	$26.74\%$	$(26.58\%,26.87\%)$	$30.78\%$	$(30.25\%,30.90\%)$	$57.56\%$	$(57.52\%,57.59\%)$
Scotland
w	$1.575$	$(1.571,1.578)$	$1.540$	$(1.540,1.542)$	$1.430$	$(1.429,1.437)$
${\mathcal{R}}_0$	$2.750$	$(2.748,2.753)$	$2.821$	$(2.820,2.833)$	$2.878$	$(2.876,2.879)$
$\mathcal{H}$	$31.00\%$	$(30.83\%,31.15\%)$	$35.36\%$	$(34.76\%,35.58\%)$	$65.26\%$	$(65.23\%,65.27\%)$
Model selection
LL	$-5801$		$-5788$		$-6220$
AIC	11616		$\mathbf{11589}$		12452

^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).