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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