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% r_eff
\newcommand{\effr}{$R_\mathrm{eff}$\xspace}
\newcommand{\effrp}{$R_\mathrm{eff}$\xspace}

% end date for r_eff estimates
\newcommand{\rpreddate}{24 January 2021 \xspace} 
% date of most recent inferred infection for r_eff estimates
\newcommand{\rinfdate}{18 January \xspace} 

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\begin{document}
\begin{table}
  \centering
  \caption*{Supplemental File 2: Parameters in the semi-mechanistic part of the time-varying model of \effrp. Prior on weights for $\omega$ correspond to Google mobility metrics in the following order: parks, residential, retail and recreation, transit stations, workplaces.}
  \label{tbl:mechpriors}
  \begin{tabular}{lr}
    \toprule
    Prior distribution & Parameter description\\
    \midrule
    \(r^{-1/2} \sim \mathrm{N^+}(0, 0.5)\) & Overdispersion of observed daily new infections\\
    \(\mathrm{logit}(p) \sim \mathrm{N}(2.57, 0.08^2)\) & Transmission probability per hour contact time\\
    \(HC_0 \sim \mathrm{N}^+(2.09, 0.06^2)\) & Baseline average daily household contacts\\
    \(NC_0 \sim \mathrm{N}^+(10.70, 0.28^2)\) & Baseline average daily non-household contacts\\
    \(HD_0 \sim \mathrm{N}^+(1.05, 1.68^2)\) & Baseline daily duration per household contact (hours)\\
    \(ND_0 \sim \mathrm{N}^+(0.687, 0.05^2)\) & Baseline daily duration per non-household contact (hours)\\
    \(\omega \sim \mathrm{N}^+(0, 1^2)\) &  Mobility-metric weights for non-household contact rates\\
    \(\alpha \sim \mathrm{N}(0, 1)\) & Effect of day of the week on non-household contact rates\\
    \(\theta \sim \mathrm{N}(0, 1)\) & Effect of day-of-week/mobility interaction on contact rate responses\\
    \(r_{NC}^{-1/2} \sim \mathrm{N^+}(0, 0.5)\) & Overdispersion of daily non-household contacts\\
    \(\mu_{\kappa_{i,0}} \sim \mathrm{N}(0, 10^2)\) & Hierarchical mean for peak microdistancing timing\\    
    \(\mu_{\kappa_{i,l}} \sim \mathrm{N}(0, 10^2)\) & Hierarchical mean for microdistancing inflection timing\\    
    \(\mu_{h_{i,l}} \sim \mathrm{N}(0, 10^2)\) & Hierarchical mean for microdistancing inflection height\\ 
    \(\sigma_{\kappa_{i,0}} \sim \mathrm{N}^+(0,0.5^2)\) & Hierarchical s.d. for peak microdistancing timing\\    
    \(\sigma_{\kappa_{i,l}} \sim \mathrm{N}^+(0,0.5^2)\) & Hierarchical s.d. for microdistancing inflection timing\\    
    \(\sigma_{h_{i,l}} \sim \mathrm{N}^+(0,0.5^2)\) & Hierarchical s.d. for microdistancing inflection height\\ 
    \(\beta \sim \mathrm{U}(0, 1)\) & Microdistancing effect on transmission\\
    \(q_1 \sim \mathrm{U}(0, 1)\) & Effect of quarantine of overseas arrivals (phase 1)\\
    \(q_2 \times q_1 \sim \mathrm{U}(0, 1)\) & Relative effect of quarantine (phase 2 vs 1)\\
    \(q_3 \times q_2 \sim \mathrm{U}(0, 1)\) & Relative effect of quarantine (phase 3 vs 2)\\
    \bottomrule
  \end{tabular}
\end{table}
\end{document}