Fig. 4: Predicting the risk threshold with a time-varying force of infection and different cumulative incidence.

Here we compute the risk threshold, which is the fold-higher risk in a high-risk group compared to a lower risk group above which a second dose to higher risk individuals is the favoured strategy and below which a first dose to lower risk individuals is favoured. We assume there is an unknown time-varying force of infection, and a given cumulative incidence rate (in the high-risk group) over a 2 year time interval (x-axis). We first calculate this assuming no waning of vaccine effectiveness by using only the estimates of vaccine effectiveness from our meta-analysis of primary studies⁴ (A). The solid line is the estimated risk threshold for each cumulative incidence, and the shaded region is the credible interval around this estimate. We also use our previous model of predicted waning of vaccine effectiveness over time, and with different dose spacing⁴ to estimate the risk threshold (B−D). In these cases, the exact risk threshold will depend on the exact time-varying force of infection, which we have chosen to leave unspecified. Thus instead of computing an exact risk-threshold we compute a range within which the actual risk threshold must be contained regardless of the exact time-varying force of infection. This range is given by the coloured region (full opacity). The credible intervals of this range are indicated by the shaded region and dashed lines. Note that above a cumulative incidence of ~75% there is no single risk threshold, thus we have truncated our estimates here.