Table 1 List of key parameters and quantities

Experimental design

\({N}_{\mathrm{group}}\)

Number of contact groups

\({N}_{\mathrm{seed}}\)

Number of seeders (initially infected individuals) in each contact group

\({N}_{\mathrm{cont}}\)

Number of contacts (initially susceptible individuals) in each contact group

\({G}_{\mathrm{size}}\)

Total number of individuals per group \({G}_{\mathrm{size}}={N}_{\mathrm{seed}}+{N}_{\mathrm{cont}}\)

\({N}_{\mathrm{total}}\)

Total number of individuals \({N}_{\mathrm{total}}={N}_{\mathrm{group}}\times {G}_{\mathrm{size}}\)

\({H}_{\mathrm{seed},z}\), \({H}_{\mathrm{cont},z}\)

Proportion of homozygotes (i.e. AA or BB) in the seeders and contacts, respectively, for group \(z\)

\(\langle {H}_{\mathrm{seed}}\rangle\), \(\langle {H}_{\mathrm{cont}}\rangle\)

Average proportion of homozygotes across groups

\({\chi }_{\mathrm{seed},z}\), \({\chi }_{\mathrm{cont},z}\)

Homozygote balance (i.e. the proportion of AA individuals minus the proportion of BB individuals) in the seeders and contacts, respectively. E.g. \({\chi }_{\mathrm{seed}}\) =1 (− 1) if the seeder population consists of AA (BB) individuals only, and \({\chi }_{\mathrm{seed}}\) = 0 if the seeder population consists of an equal number of AA and BB individuals

\(\langle {\chi }_{\mathrm{seed}}\rangle\), \(\langle {\chi }_{\mathrm{cont}}\rangle\)

Average homozygote balance across groups

Population-wide epidemiological parameters

\(\beta\)

Population average transmission rate

\(\gamma\)

Population average recovery rate

\(k\)

Shape parameter that characterises the dispersion in infection durations of different individuals

Individual-based epidemiological traits for individual \(j\)

\({\lambda }_{j}\)

Force of infection (probability per unit time to become infected)

\({w}_{j}\)

Mean of gamma distributed recovery time

\({g}_{j}\), \({f}_{j}\),\({r}_{j}\)

Fractional deviation in susceptibility, infectivity and recoverability

SNP

\({g}_{j}^{\mathrm{SNP}}\), \({f}_{j}^{\mathrm{SNP}}\),\({r}_{j}^{\mathrm{SNP}}\)

SNP-based contribution to \({g}_{j}\), \({f}_{j}\),\({r}_{j}\)

\({a}_{g}\), \({a}_{f}\),\({a}_{r}\)

SNP effects, i.e. half the change in \({g}_{j}\), \({f}_{j}\), \({r}_{j}\) comparing the AA and BB genotypes

\({\Delta }_{g}\), \({\Delta }_{f}\),\({\Delta }_{r}\)

Scaled dominance factors (1 = A is completely dominant over B, -1 = B is dominant over A, 0 = no dominance)

Fixed effects

\({\mathbf{b}}_{{\varvec{g}}}\), \({\mathbf{b}}_{{\varvec{f}}}\),\({\mathbf{b}}_{{\varvec{r}}}\)

Vectors of fixed effects for the three traits

\(\mathbf{X}\)

Design matrix for fixed effects

Residuals

\({{\varvec{\upvarepsilon}}}_{{\varvec{g}}}\), \({{\varvec{\upvarepsilon}}}_{{\varvec{f}}}\),\({{\varvec{\upvarepsilon}}}_{{\varvec{r}}}\)

Residual contributions to \(\mathbf{g}\), \(\mathbf{f}\), \(\mathbf{r}\) (coming from sources other than the SNP, fixed or group effects)

\({\varvec{\Sigma}}\)

Covariance matrix of residual contributions

Group effects

\({G}_{z}\)

Group effects (accounts for differences in transmission rates in different contact groups)

\({\upsigma }_{G}\)

Standard deviation in group effects

Bayesian model

\(\uptheta\)

Set of all model parameters

\(\upxi\)

Set of all events (infection and recovery / death times) which may be unknown, i.e. latent variables in the model

Other parameters used in the analyses

\({N}_{I}\)

Total number of infections during experiment

\(\phi\)

Fraction of contacts that become infected

\(h\)

Proportion of the total number of infections accounted for by seeders, i.e.\(h={N}_{\mathrm{seed}}/({N}_{\mathrm{seed}}+\phi {N}_{\mathrm{cont}})\)

\(\mathbf{M}\)

Fisher information matrix

\(\langle \dots \rangle\)

Average over contact groups

\(\overline{\dots }\)

Average over entire infected population (included seeders as well as those individuals infected during epidemics)