Table 2.

Model parameters estimated by Bayesian inference based on daily deaths until 1 July 2020, assuming constant ${\mathcal{R}}_{\mathrm{c}}(t)$ from first lockdown onwards (i.e., $T_2\to \infty$). 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. $T_0$ and $T_2$ parameterise linear reduction and increase in transmissibility, respectively, before and after first lockdown (larger T$\iff$ lower slope; Fig. 6).

	Heterogeneous susceptibility		Heterogeneous connectivity		Homogeneous
	Median	$95\%$ CI	Median	$95\%$ CI	Median	$95\%$ CI
Common parameters
$c_1$a	$0.2471$	$(0.2286,0.2647)$	$0.2466$	$(0.2288,0.2641)$	$0.2267$	$(0.2164,0.2370)$
$\eta$b	15	$\{15\}$	15	$\{15\}$	15	$\{15\}$
$\nu$c	$1.382$	$(0.6952,1.762)$	$0.9684$	$(0.5005,1.241)$	0	–
England
$T_0$	$-14.28$	$(-14.97,-12.40)$	$-14.31$	$(-14.97,-12.48)$	$-12.75$	$(-14.77,-10.62)$
${\mathcal{R}}_0$	$3.424$	$(3.285,3.486)$	$3.426$	$(3.291,3.485)$	$3.314$	$(3.163,3.477)$
$\mathcal{H}$	$34.48\%$	$(25.15\%,56.91\%)$	$34.83\%$	$(25.32\%,56.47\%)$	$69.83\%$	$(68.38\%,71.24\%)$
Scotland
$T_0$	$-2.506$	$(-4.053,-2.021)$	$-2.511$	$(-4.072,-2.020)$	$-2.547$	$(-4.613,-2.020)$
${\mathcal{R}}_0$	$3.365$	$(3.311,3.460)$	$3.366$	$(3.313,3.458)$	$3.370$	$(3.304,3.505)$
$\mathcal{H}$	$34.09\%$	$(25.30\%,56.69\%)$	$34.43\%$	$(25.45\%,56.24\%)$	$70.32\%$	$(69.73\%,71.47\%)$
Model selection
LL	$-1120$		$-1131$		$-3380$
AIC	$\mathbf{2254}$		2277		6772

^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).