Figure 4: SARS-CoV-2 transmission in England and Scotland with individual variation in exposure to infection.

Connectivity factors implemented as gamma distributions (reduced model (17)–(20)). Modelled trajectories of COVID-19 deaths (black) and cumulative percentage infected (blue). Dots are data for daily reported deaths: fitted (green); out-of-sample (red). Basic reproduction numbers under control $\left({\mathcal{R}}_{\text{c}}\right)$ displayed in shallow panels underneath the main plots. Left panels represent fitted segments as solid curves and projected scenarios as dashed. Right panels prolong those projections further in time assuming ${\mathcal{R}}_{\text{c}}\left(t\right)={\mathcal{R}}_0$. Input parameters: progression from E to I (δ = 1/5.5 per day); recovery (γ = 1/4 per day); relative infectiousness between E and I stages (ρ = 0.5); and IFR (ϕ = 0.9%). Initial basic reproduction numbers, coefficients of variation and control parameters estimated by Bayesian inference (estimates in Table 1). Fitted curves represent best fitting trajectories and shades are 95% credible intervals generated from 10, 000 posterior samples.