Fig. 2: Multi-scale modelling of the COVID-19 outbreak risk under annual booster vaccination.

A Log IgG(S) antibody titre relative to time since (most recent) vaccine dose. The curve shows the mean log titre (calculated over model-simulated antibody dynamics profiles for a synthetic cohort of 10,000 individuals), and the shaded region represents pointwise 95% prediction intervals (PIs) for individual antibody titres. B Relative susceptibility to SARS-CoV-2 infection following vaccination (compared to unvaccinated individuals, who are assumed to have relative susceptibility 1), which was assumed to be a function of individual antibody titre. The curve shows the mean susceptibility, and the shaded region represents pointwise 95% PIs for individual susceptibility. C Top: population-average susceptibility, \({\eta }_{t}\), as a function of calendar time, \(t\), assuming 60% of the population receives booster vaccines between 1 October and 15 December each year (this time period is shown in the grey shaded regions). Bottom: instantaneous reproduction number, \({R}_{0,t}\), in the absence of booster vaccination. The instantaneous reproduction number when booster vaccination takes place, \({R}_{t}={{\eta }_{t}R}_{0,t}\), is shown in Supplementary Fig. 2. D Outbreak risk, \({p}_{t}\), following the introduction of a single newly infected individual on day \(t\), both without (blue dashed curve) and with (orange curve) booster vaccination, calculated using our analytical approach.