case_images: PMC9053223_01
case_images: The epidemiological model used in our analyses.. a Following the introduction of an infected individual into the host population, local transmission may happen with each infected individual generating new infections at rate , where  reflects the vaccination coverage in the local population. The mean infectious period of infected individuals is  days, and the rates shown are per infected individual. b The vaccination process is modelled by setting  according to the proportion of individuals in the population who have been vaccinated with one () or two () doses. The first vaccine dose is assumed to have effectiveness  and the second vaccine dose has effectiveness , where the values of  and  are the multiplicative reductions in the susceptibility of individuals who have been vaccinated with one or two vaccine doses, respectively (compared to an unvaccinated host). Vaccine doses are effective  days after they are administered. This leads to declining population susceptibility as a vaccine is rolled out across the population.
case_images: 43856_2021_38_Fig1_HTML.jpg
case_images: PMC9053223_01_43856_2021_38_Fig1_HTML.jpg
case_images: Fig1
case_images: This result is robust to a range of assumptions surrounding virus transmission and the effectiveness of vaccines (Figs S1-S4).
case_images: Effect of vaccination on population susceptibility.. a The proportion of the population of the Isle of Man that is unvaccinated (), vaccinated with a single dose () and vaccinated with two doses (). The period in which vaccination data were available is shown in white, and the period in which vaccination data were projected is shown in purple. b The time-dependent reproduction number () corresponding to the vaccination data in panel a with all travel restrictions and non-pharmaceutical interventions removed, starting from a mean initial value of  To account for uncertainty in the value of , a normal distribution was assumed about the mean value of  with variance , which is reflective of the range of  values estimated early in the COVID-19 pandemic. c Analogous to panel b but starting from a mean initial value of . d-f Analogous to panels a-c but using vaccination data for Israel. In all panels,  days corresponds to 18th December 2020. Ticks on the x-axes refer to the starts of the months labelled. Parameter values are shown in Table 1.
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case_images: PMC9053223_01_43856_2021_38_Fig2_HTML.jpg
case_images: Fig2
case_images: For each metric, and each time during the vaccination programme, we calculated the outbreak risk by integrating over the full distribution for  shown in Fig. 2. This result is robust to a range of assumptions surrounding virus transmission and the effectiveness of vaccines (Figs S1-S4).
case_images: The risk that an infectious case introduced at each stage of the vaccination campaign initiates an outbreak, if travel restrictions and other non-pharmaceutical interventions are removed.. a The outbreak risk was assessed using the four metrics (Instantaneous Outbreak Risk - black; Case Outbreak Risk - blue dashed; Simulated Outbreak Risk - green dots; Numerical Outbreak Risk - red), based on vaccination data from the Isle of Man and assuming mean , as in Fig. 2b. The period in which vaccination data were available is shown in white, and the period in which vaccination data were projected is shown in purple. b Analogous to panel a but with a mean  (see Fig. 2c). c Analogous to panel a but using vaccination data for Israel (see Fig. 2e). d Analogous to panel a but using vaccination data for Israel with a mean  (see Fig. 2f). Ticks on the x-axes refer to the starts of the months labelled. Parameter values are shown in Table 1.
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case_images: PMC9053223_01_43856_2021_38_Fig3_HTML.jpg
case_images: Fig3
case_images: We then calculated the values of the four different outbreak risk metrics throughout the period considered (18th December 2020 to 20th August 2021) based on these vaccination projections (Fig. 3). For that reason, it is unsurprising that the IOR sometimes overestimates the outbreak risk compared to the other risk metrics (see e.g. black lines in Fig. 3a, c - and see Discussion). This result is robust to a range of assumptions surrounding virus transmission and the effectiveness of vaccines (Figs S1-S4).