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‎.gitignore‎

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‎doc/perturbation-supp.pdf‎

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‎doc/perturbation-supp.tex‎

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\documentclass[12pt]{article}
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% \usepackage[top=1in,left=1in, right = 1in, footskip=1in]{geometry}
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\usepackage[top=1in,footskip=1in]{geometry}
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\usepackage{graphicx}
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\usepackage{xspace}
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%\usepackage{adjustbox}
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\usepackage{multirow}
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\usepackage{booktabs}
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\usepackage{pdflscape}
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\usepackage{grffile}
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\newcommand{\comment}{\showcomment}
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%% \newcommand{\comment}{\nocomment}
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\newcommand{\showcomment}[3]{\textcolor{#1}{\textbf{[#2: }\textsl{#3}\textbf{]}}}
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\newcommand{\nocomment}[3]{}
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\newcommand{\jd}[1]{\comment{cyan}{JD}{#1}}
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\newcommand{\swp}[1]{\comment{magenta}{SWP}{#1}}
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\newcommand{\bmb}[1]{\comment{blue}{BMB}{#1}}
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\newcommand{\djde}[1]{\comment{red}{DJDE}{#1}}
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\newcommand{\eref}[1]{Eq.~(\ref{eq:#1})}
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\newcommand{\fref}[1]{Fig.~\ref{fig:#1}}
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\newcommand{\Fref}[1]{Fig.~\ref{fig:#1}}
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\newcommand{\sref}[1]{Sec.~\ref{#1}}
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\newcommand{\frange}[2]{Fig.~\ref{fig:#1}--\ref{fig:#2}}
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\newcommand{\tref}[1]{Table~\ref{tab:#1}}
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\newcommand{\tlab}[1]{\label{tab:#1}}
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\newcommand{\seminar}{SE\mbox{$^m$}I\mbox{$^n$}R}
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\usepackage{amsthm}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{amsfonts}
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\usepackage[utf8]{inputenc} % make sure fancy dashes etc. don't get dropped
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\usepackage{lineno}
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\linenumbers
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\usepackage[pdfencoding=auto, psdextra]{hyperref}
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\usepackage{natbib}
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\bibliographystyle{chicago}
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\date{\today}
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\usepackage{xspace}
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\newcommand*{\ie}{i.e.\@\xspace}
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\usepackage{color}
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\newcommand{\Rx}[1]{\ensuremath{{\mathcal R}_{#1}}\xspace}
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\newcommand{\RR}{\ensuremath{{\mathcal R}}\xspace}
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\newcommand{\Rres}{\Rx{\mathrm{res}}}
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\newcommand{\Rinv}{\Rx{\mathrm{inv}}}
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\newcommand{\Rhat}{\ensuremath{{\hat\RR}}}
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\newcommand{\Rt}{\ensuremath{{\mathcal R}(t)}\xspace}
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\newcommand{\tsub}[2]{#1_{{\textrm{\tiny #2}}}}
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\newcommand{\dd}[1]{\ensuremath{\, \mathrm{d}#1}}
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\newcommand{\dtau}{\dd{\tau}}
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\newcommand{\dx}{\dd{x}}
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\newcommand{\dsigma}{\dd{\sigma}}
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\newcommand{\rx}[1]{\ensuremath{{r}_{#1}}\xspace}
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\newcommand{\rres}{\rx{\mathrm{res}}}
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\newcommand{\rinv}{\rx{\mathrm{inv}}}
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\newcommand{\psymp}{\ensuremath{p}} %% primary symptom time
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\newcommand{\ssymp}{\ensuremath{s}} %% secondary symptom time
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\newcommand{\pinf}{\ensuremath{\alpha_1}} %% primary infection time
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\newcommand{\sinf}{\ensuremath{\alpha_2}} %% secondary infection time
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\newcommand{\psize}{{\mathcal P}} %% primary cohort size
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\newcommand{\ssize}{{\mathcal S}} %% secondary cohort size
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\newcommand{\gtime}{\tau_{\rm g}} %% generation interval
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\newcommand{\gdist}{g} %% generation-interval distribution
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\newcommand{\idist}{\ell} %% incubation-period distribution
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\newcommand{\total}{{\mathcal T}} %% total number of serial intervals
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\usepackage{lettrine}
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\newcommand{\dropcapfont}{\fontfamily{lmss}\bfseries\fontsize{26pt}{28pt}\selectfont}
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\newcommand{\dropcap}[1]{\lettrine[lines=2,lraise=0.05,findent=0.1em, nindent=0em]{{\dropcapfont{#1}}}{}}
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\begin{document}
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\begin{flushleft}{
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\Large
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\textbf\newline{
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Supplementary Information for \textit{Interplay between climate and childhood mixing can explain a sudden shift in RSV seasonality in Japan}
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}
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}
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\newline
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\\
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Sang Woo Park\textsuperscript{1,2,3,*}, Inga Holmdahl\textsuperscript{3,4}, Emily Howerton\textsuperscript{3}, Wenchang Yang\textsuperscript{5}, Rachel E. Baker\textsuperscript{6}, Gabriel A. Vecchi\textsuperscript{4,5,7}, Sarah Cobey\textsuperscript{2}, C. Jessica E. Metcalf\textsuperscript{3,4,8}, Bryan T. Grenfell\textsuperscript{3,4,8}
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\\
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\bigskip
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\textbf{1} School of Biological Sciences, Seoul National University, Seoul, Korea
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\\
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\textbf{2} Department of Ecology and Evolution, University of Chicago, Chicago, IL, USA
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\\
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\textbf{3} Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA
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\\
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\textbf{4} High Meadows Environmental Institute, Princeton University, Princeton, NJ, USA
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\\
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\textbf{5} Department of Geosciences, Princeton University, Princeton, NJ, USA
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\\
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\textbf{6} Department of Epidemiology, Brown School of Public Health, Brown University, Providence, Rhode Island, USA
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\\
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\textbf{7} Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ, USA
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\\
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\textbf{8} Princeton School of Public and International Affairs, Princeton, NJ, USA
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\bigskip
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*Corresponding author: sangwoopark@snu.ac.kr
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\end{flushleft}
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\pagebreak
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\setcounter{figure}{0}
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\setcounter{equation}{0}
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\renewcommand{\thefigure}{S\arabic{figure}}
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\renewcommand{\theequation}{S\arabic{equation}}
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\renewcommand{\thetable}{S\arabic{table}}
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\section*{Supplementary Materials}
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\subsection*{Supplementary Table}
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\begin{table}[ht]
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\centering
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\begin{tabular}{l|l|l|r}
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\hline
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\textbf{Island} & \textbf{Variable} & \textbf{Coefficient} & \textbf{p-value} \\
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\hline
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\multirow{5}{*}{Hokkaido} & Intercept & 4.28*** & $7.28\times 10^{-5}$ \\
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& Humidity & 1.26** & 0.0011 \\
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& Humidity$^2$ & -0.02 & 0.082 \\
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& Temperature & -0.13 & 0.051 \\
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& Temperature$^2$ & -0.02*** & $7.75 \times 10^{-6}$ \\
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\hline
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\multirow{5}{*}{Honshu} & Intercept & 6.73*** & $5.4 \times 10^{-13}$ \\
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& Humidity & 0.38 & 0.19 \\
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& Humidity$^2$ & 0.03* & 0.011 \\
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& Temperature & 0.03 & 0.80 \\
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& Temperature$^2$ & -0.02*** & $0.00012$ \\
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\hline
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\multirow{5}{*}{Shikoku} & Intercept & 12.25*** & $<2 \times 10^{-16}$ \\
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& Humidity & 0.43 & 0.30 \\
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& Humidity$^2$ & -0.01 & 0.67 \\
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& Temperature & -0.84*** & $0.00021$ \\
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& Temperature$^2$ & 0.02* & 0.013 \\
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\hline
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\multirow{5}{*}{Kyushu} & Intercept & 9.91*** & $<2 \times 10^{-16}$ \\
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& Humidity & 0.52 & 0.068 \\
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& Humidity$^2$ & 0.01 & 0.27 \\
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& Temperature & -0.59*** & $0.00046$ \\
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& Temperature$^2$ & 0.00 & 0.60 \\
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\hline
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\multirow{5}{*}{Ryukyu} & Intercept & 14.07 & 0.056 \\
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& Humidity & -0.90 & 0.060 \\
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& Humidity$^2$ & 0.04** & $0.0073$ \\
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& Temperature & 0.15 & 0.86 \\
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& Temperature$^2$ & -0.01 & 0.56 \\
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\hline
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\end{tabular}
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\caption{
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\textbf{Bivariate quadratic regression of estimated transmission rate against mean specific humidity and mean temperature.}
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P-values were obtained from a two-sided t-test based on the estimated standard errors from the regression model.
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We did not adjust for multiple comparisons.
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*$p<0.05$, **$p<0.01$, ***$p<0.001$.
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}
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\end{table}
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\pagebreak
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\begin{table}[ht]
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\centering
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\begin{tabular}{l|l|l}
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\hline
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\textbf{Island} & \textbf{Humidity model} & \textbf{Temperature model} \\
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\hline
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Hokkaido & 0.44 & 0.52\\
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\hline
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Honshu & 0.39 & 0.29\\
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\hline
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Shikoku & 0.63 & 0.72\\
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\hline
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Kyushu & 0.77 & 0.77\\
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\hline
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Ryukyu & 0.59 & 0.47\\
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\hline
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\end{tabular}
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\caption{
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\textbf{Comparisons of R squared values from univariate quadratic regression of estimated transmission rate against mean specific humidity and mean temperature.}
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}
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\end{table}
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\pagebreak
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\subsection*{Supplementary Figures}
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\begin{figure}[!pth]
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\includegraphics[width=\textwidth]{../figure/figure1_cog.pdf}
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\caption{
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\textbf{Estimates of center of gravity (i.e., the mean timing of an epidemic) across all prefectures, stratified by island.}
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Hokkaido and Ryukyu islands each contain only one prefectures: Hokkaido and Okinawa, respectively.
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The center (horizontal line), lower bounds, and upper bounds of the box plot correspond to median, lower quartile (25th percentile), and upper quartile (75th percentile), respectively.
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The whiskers indicate the range of values that extend up to 1.5 times the interquartile range beyond the lower and upper quartiles.
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Outliers, which fall outside this range, are plotted individually.
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}
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\end{figure}
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\begin{figure}[!pth]
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\includegraphics[width=\textwidth]{../figure/figure_map.pdf}
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\caption{
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\textbf{Colored map of Japan.}
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Each of five major islands are marked by different colors.
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}
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\end{figure}
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\pagebreak
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\begin{figure}[!pth]
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\includegraphics[width=\textwidth]{../figure/figure_joint_climate.pdf}
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\caption{
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\textbf{Joint relationship between the estimated periodic seasonal transmission rates and mean specific humidity across all five islands.}
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Points represent the estimates across 52 weeks in each island.
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The line represent a generalized additive model fit using cubic spline basis.
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Shaded regions represent the corresponding 95\% confidence intervals (n=260).
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}
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\end{figure}
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\pagebreak
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\begin{figure}[!pth]
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\includegraphics[width=\textwidth]{../figure/figure_comb_sirs_npi_temp.pdf}
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\caption{
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\textbf{Relationship between the estimated periodic seasonal transmission rates and mean temperature.}
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Points represent seasonal transmission rate estimates across 52 weeks versus average humidity across 2013--2020.
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Blue lines and regions represent the corresponding locally estimated scatterplot smoothing (LOESS) estimates and corresponding 95\% confidence intervals (n=52).
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Red lines and regions represent the corresponding quadratic regression fits and corresponding 95\% confidence intervals (n=52).
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}
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\end{figure}
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\pagebreak
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\begin{figure}[!pth]
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\includegraphics[width=\textwidth]{../figure/figure_comb_sirs_npi_temp_hum.pdf}
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\caption{
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\textbf{Relationship between the mean weekly temperature and mean weekly humidity.}
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}
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\end{figure}
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\pagebreak
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\begin{figure}[!pth]
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\begin{center}
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\includegraphics[width=0.8\textwidth]{../figure/figure_ryukyu_sirs_change.pdf}
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\caption{
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\textbf{A lack of increase in susceptible pool explains constant seasonality in Ryukyu island.}
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(A) Predicted effects of the proportion of infected $i(0)$ and susceptible $S(0)$ at the beginning of season on center of gravity.
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Points represent the estimated values for $i(0)$ and $s(0)$ between 2013 and 2019, showing the last two digits of a given year.
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The white vertical dashed line represents the $i(0)$ value used for simulating epidemic dynamics in panel B.
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(B) Changes in epidemic trajectories that would be caused by an increase in the susceptible proportion at the beginning of season for a fixed value of $i(0)$.
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}
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\end{center}
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\end{figure}
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\pagebreak
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\begin{figure}[!pth]
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\begin{center}
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\includegraphics[width=0.8\textwidth]{../figure/figure_hokkaido_sirs_change.pdf}
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\caption{
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\textbf{Estimated change in susceptibility for Hokkaido island and counterfactual simulations assuming an increased susceptibility.}
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(A) Predicted effects of the proportion of infected $i(0)$ and susceptible $s(0)$ at the beginning of season on center of gravity.
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Points represent the estimated values for $i(0)$ and $s(0)$ between 2013 and 2019, showing the last two digits of a given year.
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The white vertical dashed line represents the $i(0)$ value used for simulating epidemic dynamics in panel B.
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(B) Changes in epidemic trajectories that would be caused by an increase in the susceptible proportion at the beginning of season for a fixed value of $i(0)$.
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}
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\end{center}
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\end{figure}
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\pagebreak
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\begin{figure}[!pth]
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\includegraphics[width=\textwidth]{../figure/figure_comb_sirs_npi2.pdf}
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\caption{
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\textbf{Summary of SIRS model fits to RSV outbreaks across major islands in Japan.}
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(A) Comparisons of observed cases (points) across the five major islands and fitted epidemic trajectories (red lines).
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(B) Estimated periodic seasonal transmission rates before (red) and after (blue) the change in seasonality of RSV outbreaks.
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(C) Estimated proportion of the susceptible pool over time.
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In panels A--C, lines represent the estimated median of the posterior distribution (n=8000).
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In panels A--C, shaded regions represent the 95\% credible intervals from the posterior distribution (n=8000).
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(D) Estimated proportion of the susceptible pool on the 26th week of each year.
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Points represent median from n=8000 posterior samples.
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Error bars represent the 95\% credible interval in our estimates (n=8000 posterior samples).
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}
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\end{figure}
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\pagebreak
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\bibliography{perturbation}
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\end{document}

‎doc/perturbation.pdf‎

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‎doc/perturbation.tex‎

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\textbf{Summary of SIRS model fits to RSV outbreaks across major islands in Japan.}
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(A) Comparisons of observed cases (points) across the five major islands and fitted epidemic trajectories (red lines).
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(B) Estimated periodic seasonal transmission rates.
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Lines represent the estimated median of the posterior distribution (n=8000 posterior samples).
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Shaded regions represent the 95\% credible intervals from the posterior distribution (n=8000 posterior samples).
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(C) Relationship between the estimated periodic seasonal transmission rates and mean specific humidity.
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Points represent seasonal transmission rate estimates across 52 weeks versus average humidity across 2013--2020.
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Blue lines and regions represent the corresponding locally estimated scatterplot smoothing (LOESS) estimates and corresponding 95\% confidence intervals (n=52).
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Red lines and regions represent the corresponding quadratic regression fits and corresponding 95\% confidence intervals (n=52).
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(D) Estimated relative changes in transmission, capturing the impact of NPI measures.
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Lines represent the estimated median of the posterior distribution (n=8000 posterior samples).
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Shaded regions represent the 95\% credible intervals from the posterior distribution (n=8000 posterior samples).
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(E) Estimated proportion of the susceptible pool.
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Lines represent the estimated median of the posterior distribution (n=8000 posterior samples).
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Shaded regions represent the 95\% credible intervals from the posterior distribution (n=8000 posterior samples).
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In panels B, D, and E, lines represent the estimated median of the posterior distribution (n=8000 posterior samples).
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In panels B, D, and E, shaded regions represent the 95\% credible intervals from the posterior distribution (n=8000 posterior samples).
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}
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\label{fig:fig2}
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\end{figure}

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