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Table 2 Prior distributions and initial values (obtained from CIPHA data) used for model fits

From: Effectiveness of the BNT162b2 (Pfizer-BioNTech) and the ChAdOx1 nCoV-19 (Oxford-AstraZeneca) vaccines for reducing susceptibility to infection with the Delta variant (B.1.617.2) of SARS-CoV-2

(a) Prior distributions used for initialising model fits
Name \(\bf {\gamma}\) Prior distributions Initial values
\(\bf {\beta}\) \(\bf {I,I_{ij}}\) \(\bf {e_{ij},\mu _{i}}\) \(\bf {S,S_{ij},R,R_{ij}}\)
Core Model 1/7 \(\text {Unif}[0,10]\) \(\text {Unif}[0,100]\) \(\text {Unif}[0,1]\) Table 2b
Sensitivity to \(\gamma\) 1/3 \(\text {Unif}[0,10]\) \(\text {Unif}[0,100]\) \(\text {Unif}[0,1]\) Table 2b
Sensitivity to \(\gamma\) 1/11 \(\text {Unif}[0,10]\) \(\text {Unif}[0,100]\) \(\text {Unif}[0,1]\) Table 2b
Double Removed 1/7 \(\text {Unif}[0,10]\) \(\text {Unif}[0,100]\) \(\text {Unif}[0,1]\) Table 2c
(b) Initial values when assuming all infected from start of pandemic moved to removed class
S \(\bf {S_{1A}}\) \(\bf {S_{2A}}\) \(\bf {S_{1P}}\) \(\bf {S_{2P}}\) R \(\bf {R_{1A}}\) \(\bf {R_{2A}}\) \(\bf {R_{1P}}\) \(\bf {R_{2P}}\)
1266979 478347 312594 74665 384481 70887 42715 20895 6738 26715
(c) Initial values when assuming infected individuals are underestimated by 50%
S \(\bf {S_{1A}}\) \(\bf {S_{2A}}\) \(\bf {S_{1P}}\) \(\bf {S_{2P}}\) R \(\bf {R_{1A}}\) \(\bf {R_{2A}}\) \(\bf {R_{1P}}\) \(\bf {R_{2P}}\)
1196092 435632 291699 67927 357766 141774 85430 41790 13476 53430
  1. Notation is as follows \(\beta\): Transmission rate, \(\gamma\): Recovery rate, \(e_{ij}\): Effectiveness of i doses of vaccine j against infection, S: Unvaccinated susceptible individuals, \(S_{ij}\): Susceptible individuals who have received i doses of vaccine j, I: Unvaccinated infected individuals, \(I_{ij}\): Infected individuals who have received i doses of vaccine j, R: Unvaccinated removed individuals, \(R_{ij}\): Removed individuals who have received i doses of vaccine j, and \(\mu _i\): Infectiveness of an infected individual with i doses of either vaccine. For number of doses we have \(i\in \{1,2\}\) and for vaccines \(j\in \{A,P\}\) for Oxford-AstraZeneca and Pfizer-BioNTech respectively