\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}



\usepackage{float}








\begin{document}

\title{Supercritical and homogenous transmission of monkeypox in the capital of
China.}



\author[1]{Yunjun Zhang}%
\author[1]{Xiao-Hua Zhou}%
\affil[1]{Peking University School of Public Health}%


\vspace{-1em}



  
  \date{May 27, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
\textbf{Background}: Starting from May 31 \textsuperscript{st}, 2023,
the local transmission of monkeypox (Mpox) in mainland China began in
Beijing. Till now, the transmission characteristics have not been
explored. \textbf{Method}: Based on the daily Mpox incidence data in the
first three weeks of Beijing (from May 31 \textsuperscript{st} to June
21 \textsuperscript{st}, 2023) , we employed the instant-individual
heterogeneity transmission model to simultaneously calculate the
effective reproduction number ( \emph{R} \textsubscript{e}) and the
degree of heterogeneity ( \emph{k}) of the Beijing epidemic. We
additionally simulated the monthly infection size in Beijing from July
to September and compared with the reported data to project subsequent
transmission dynamics. \textbf{Results}: We estimated \emph{R}
\textsubscript{e} to be 1.68 {[}95\% HPD:1.12, 2.41{]}, and \emph{k} to
be 2.57 {[}95\% HPD: 0.54, 83.88{]}, suggesting the transmission of Mpox
in Beijing was supercritical and didn't have considerable transmission
heterogeneity. We projected that \emph{R} \textsubscript{e} fell in the
range of 0.95 to 1.0 from July to September, highlighting more efforts
needed to further reduce the Mpox transmissibility. \textbf{Conclusion}:
Our findings revealed supercritical and homogeneous transmission of the
Mpox epidemic in Beijing. Our results may provide reference for
understanding and predicting of the on-going Mpox transmission in other
regions of China and assess the effect of control measures.%
\end{abstract}%



\sloppy


\textbf{Title} : Supercritical and homogenous transmission of monkeypox
in the capital of China.

\textbf{Yunjun ZhangI1,2 and Xiaohua ZhouI1,2,3,4}

1 Department of Biostatistics, School of Public Health, Peking
University, Beijing, China,

2 Center for Statistical Science, Peking University, Beijing, China,

3 Beijing International Center for Mathematical Research, Peking
University, Beijing, China,

4 School of Mathematical Sciences, Peking University, Beijing, China

Correspondence:

Yunjun Zhang School of Public Health, Peking University, Beijing, China.

Email: yunjun.zhang@pku.edu.cn



\textbf{ABSTRACT}

\textbf{Background} : Starting from May 31\textsuperscript{st}, 2023,
the local transmission of monkeypox (Mpox) in mainland China began in
Beijing. Till now, the transmission characteristics have not been
explored.

\textbf{Method} : Based on the daily Mpox incidence data in the first
three weeks of Beijing (from May 31\textsuperscript{st} to June
21\textsuperscript{st}, 2023) , we employed the instant-individual
heterogeneity transmission model to simultaneously calculate the
effective reproduction number (\emph{R} \textsubscript{e}) and the
degree of heterogeneity (\emph{k} ) of the Beijing epidemic. We
additionally simulated the monthly infection size in Beijing from July
to September and compared with the reported data to project subsequent
transmission dynamics.

\textbf{Results} : We estimated \emph{R} \textsubscript{e} to be 1.68
{[}95\% HPD:1.12, 2.41{]}, and \emph{k} to be 2.57 {[}95\% HPD: 0.54,
83.88{]}, suggesting the transmission of Mpox in Beijing was
supercritical and didn't have considerable transmission heterogeneity.
We projected that \emph{R} \textsubscript{e} fell in the range of 0.95
to 1.0 from July to September, highlighting more efforts needed to
further reduce the Mpox transmissibility.

\textbf{Conclusion} : Our findings revealed supercritical and
homogeneous transmission of the Mpox epidemic in Beijing. Our results
may provide reference for understanding and predicting of the on-going
Mpox transmission in other regions of China and assess the effect of
control measures.

\textbf{KEYWORDS}

monkeypox, effective reproduction number, transmission heterogeneity

\textbf{Introduction}

Since May 2022, the monkeypox (Mpox ) epidemic has caused 90618 cases
and 157 deaths in 115 countries and regions {[}1{]}. At present, the
epidemic in most areas is nearing its end. However, China was not
affected by Mpox in 2022 because of its strict border quarantine and
inbound traveler isolation policies, which had been applied since 2020
against coronavirus disease (COVID-19). Therefore, the spread of Mpox in
mainland China is considerably lagging behind other countries. When the
control policies were relieved in 2023, mainland China reported a
significant increase in Mpox cases, with the first locally acquired case
of Mpox confirmed in Beijing on May 31, 2023 {[}2{]}. Till 2023-09-30,
there have been 1403 reported Mpox cases in mainland China, of which 222
cases were in Beijing {[}3{]}. Phylogenetic analysis also indicated the
local strains transmitted in Beijing belonged to the West African
lineage {[}4{]}.

To estimate the development of Mpox epidemic and to design appropriate
control measures, it is essential to understand the dynamics (i.e.,
effective reproduction number and dispersion number (\emph{k} )) of Mpox
transmission in mainland China. Effective reproduction number, denoted
as \emph{R} \textsubscript{e}, represents the average number of
secondary cases caused by a primary case in a partly susceptible
population {[}5{]}. \emph{R} \textsubscript{e} \textgreater{}1 suggests
the further infection is likely without stricter control measures.

In addition, the dispersion number \emph{k} , representing the variation
of the distribution of secondary cases, is an empirical measure of
transmission heterogeneity {[}6,7{]}. A small \emph{k} (i.e.,
k\textless{}1) indicates a high degree of transmission heterogeneity,
indicating probability of a superspreading event (SSE) with one
individual infecting a greater number of secondary cases than average.
This was reported in the 1980-84 Mpox epidemic in West Africa {[}8{]}.
Therefore, evaluation of transmission heterogeneity may also aid
prevention efforts and reduce future infections.

In the past five months since the confirmation of the first Mpox in
Beijing, there has not been a report of the transmission dynamics of
this epidemic. The current study was to analyze the transmission
characteristics based on an epidemiological report of confirmed daily
Mpox cases from 05-31 to 06-21, 2023 in Beijing {[}4{]}. Specifically,
we employed the instant-individual heterogeneity transmission model
{[}6{]} to analyze the daily incidence to reveal\emph{R}
\textsubscript{e} and \emph{k} of Beijing Mpox epidemic in the first
three weeks. As the daily incidence thereafter was not available, we
simulated the subsequent infection size in Beijing from July to
September to project subsequent transmission dynamics. Our results will
shed light on the on-going Mpox epidemic in mainland China and provide
reference for policy making and public response.

\textbf{Materials and Methods}

\textbf{Data}

A recently epidemiological study {[}4{]} reported the daily incidence of
confirmed Mpox cases in Beijing, the capital of China from 05-31 to
06-21, 2023, providing a high-resolution dataset for studying the
transmission dynamics of Mpox in Beijing. We extracted the daily
incidence of Mpox confirmed cases from this epidemiological study
{[}Figure 1A in 4{]}. We regarded the diagnosis date as the confirmed
date.

\textbf{Analytical method}

We used the individual-instant heterogeneity model {[}6{]} to analyze
the incidence data and estimated the effective reproduction number and
the dispersion number simultaneously. In the analysis ,we used the
gamma-distributed serial interval with the mean = 5.6 days and SD = 1.5
days {[}9{]}.

\textbf{Simulation study}

To predict the variation in transmission dynamics from 2023-07-01 to
2023-09-30 in Beijing, we simulated the infection data during this
period and compared with the official reports {[}3{]}. For each
simulation, we assumed constant reproduction number and constant degree
of heterogeneity which represented the average dynamics during the
period. We started with the incidence curve between 05-31 and 06-21, and
simulated the daily confirmed cases with the individual-instant
heterogeneity model as in {[}6{]} and then aggregated to generate the
monthly reports. We set three levels of reproduction number as
0.8,0.85,0.95 and 1.0, and three level of dispersion number as 1.0, 2.0,
and 3.0. For each parameter setting, we simulated the spread of Mpox for
50000 times.

\textbf{Results:}

For the Mpox epidemic from 2023-05-31 to 2023-06-21 in Beijing, we
calculated the \emph{R} \textsubscript{e} = 1.68 {[}95\% HPD:1.12,
2.41{]}, being considerably larger than the critical value of 1 (Figure
1), which is consistent with other studies on the early transmission of
Mpox in European countries {[}5{]}. We also calculate \emph{k} = 2.57
{[}95\% HPD: 0.54, 83.88{]} and the quantity of p80 (i.e., the
(smallest) fraction of individuals responsible for 80\% of secondary
infections on average) as 0.25. These quantities do not indicate high
degree of transmission heterogeneity.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1:} \textbf{Estimate of transmission dynamics of the
Monkeypox epidemic in Beijing between 2023-05-31 and 2023-06-21} . (A)
Effective reproduction number (Re); (B) Dispersion parameter (k).

Since 2023-06-21, Mpox has continued to spread in Beijing, with 81, 54,
and 42 newly confirmed cases reported in July, August, and September
respectively. Since there were no daily incidence data during this
period, we turned to simulation to project the transmission dynamics. By
assuming the serial interval as before, we found that the reported
confirmed case data from July to September were close to the simulated
data with the \emph{R} \textsubscript{e} as 0.95 and 1.0 (Figure 2B),
suggesting that the average effective reproduction number was likely to
fell in the range of 0.95 to 1.0 during this period. This result was
robust to the variation both in the dispersion parameter \emph{k}(Figure
2) and in the serial interval parameters (Figure S1).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2:} \textbf{Comparison of cumulative case data with model
projections for the 2023 Mpox epidemic in Beijing} . Cumulative case
data (black lines) between 2023-06-21 and 2023-09-30, and comparison
with projections from the individual-instant heterogeneity model under
homogeneous transmission (A\textasciitilde{}C,\emph{k}
=1\textasciitilde{}4) and heterogeneous transmission (D,\emph{k} =0.5).
Colored lines represented the medians of simulated data under various
levels of effective reproduction number\emph{R} \textsubscript{e}. In
simulation, we used the gamma-distributed serial interval with the mean
= 5.6 days and SD = 1.5 days and repeated for 5000 times.

\textbf{Discussion}

This study estimated the transmission dynamics (i.e., effective
reproduction number \emph{R} \textsubscript{e} and dispersion
number\emph{k} ) of Mpox in Beijing in the first three weeks of
transmission for the first time. The effective reproduction
number\emph{R} \textsubscript{e} was calculated to be 1.68 {[}95\%
HPD:1.12, 2.41{]} , which is higher than the threshold value of 1. And
the dispersion number \emph{k} was 2.57 {[}95\% HPD: 0.54, 83.88{]},
which is also greater than 1 and does not indicate a high risk of
transmission heterogeneity.

Compared with the transmission of the West African lineage reported
outside of China, our estimation of \emph{R}
\textsubscript{e}\textgreater{}1 for the Beijing epidemic is consistent
with that of the England (\emph{R} \textsubscript{e} = 1.60 (95\% CI:
1.50, 1.70)), Portugal (\emph{R} \textsubscript{e} =1.40 (95\% CI: 1.20,
1.60)) and Spain (\emph{R} \textsubscript{e} = 1.80 (95\% CI: 1.70,2.0)
) in May to June of 2022 {[}5{]}. Our estimates of the first three weeks
suggested that the Beijing Mpox epidemic would have additional
infections after 2023-06-21, which was evidenced by the increase in
reported new cases to 80 in July 2023 {[}3{]}. When certain measures
were subsequently adopted, the reported new cases dropped to 54 in
August and 42 in September, which corresponded to \emph{R}
\textsubscript{e} of 0.95-1.0, slightly under the threshold of 1, as
revealed by our simulation. This also indicates that additional measures
need to be taken to further reduce the transmissibility of Mpox in
Beijing. .

Another interesting feature of Beijing Mpox epidemic is the homogenous
transmission. We estimated \emph{k} = 2.57, being above the critical
value of 1, and estimated that 80\% of secondary transmissions were
likely to be caused by 25\% of primary cases, which did not invoke the
20/80 rule {[}7{]}. Our finding was consistent with the epidemiological
investigation which showed that the distribution of the close contact
among the confirmed cases in Beijing was not skewed and no SSE was
identified {[}4{]}. Similarly, another research about Mpox transmission
in the United States in 2022 also reported absence of heterogeneity and
no SSE identified {[}10{]}.

In contrast, for the 1980-84 Mpox epidemic in West Africa, several SSEs
were reported, which was closely related with the unrecognized or
misdiagnosed cases that were later documented {[}8,11{]}. Besides,
contemporary health-workers and the public have improved awareness
against Mpox infection, which reduced the risk of infection or
mis-diagnose and thereby reduced the chance of SSE {[}10{]}. In
addition, the homogenous nature of the Mpox transmission in Beijing
highlighted that more population-level intervention, for instance,
vaccines, could be effective in reducing the transmissibility of the
Mpox virus {[}7{]}.

In conclusion, we assessed the transmission dynamics in the early stage
of Mpox epidemic in Beijing, China. Our findings revealed super critical
and homogeneous transmission of the Mpox epidemic in Beijing. Our
results may provide reference for understanding and predicting of the
on-going Mpox transmission in other regions of China and assess the
effect of control measures.

\textbf{AUTHOR CONTRIBUTIONS}

Yunjun Zhang and Xiaohua Zhou designed the study. Yunjun Zhang collected
the data, built the model, carried out the analysis, and write the
original draft. Xiaohua Zhou gave critical revisions of the manuscript.
All authors read and approved the final manuscript.

\textbf{ACKNOWLEDGMENTS}

The authors are grateful to Prof Jian Zhang of Peking University and Tom
Britton of Stockholm University for the insightful discussions and the
careful examination of the manuscript.

\textbf{CONFLICT OF INTEREST}

The authors declared no conflict of interest.

\textbf{DATA AVAILABILITY STATEMENT}

All the data and codes for this study are available online:
https://github.com/yunPKU/Mpox\_BJ\_Assessment.

\textbf{REFERENCES}

\begin{enumerate}
\tightlist
\item
  2022-23 Mpox Outbreak: Global Trends. Geneva: World Health
  Organization, 2023. Available online:
  https://worldhealthorg.shinyapps.io/mpx\_global/ (last cited:
  2023-10-17)
\item
  Zhang, D., Qi, X., Li, F., Chu, Y., Wu, K., Li, J., Meng, X., Dou, X.,
  Ren, Z., Jin, H. and Li, S., 2023. The first local case of mpox caused
  by an imported case in the Chinese mainland.~\emph{Biosafety and
  Health} ,~\emph{5} (4), pp.187-190.
\item
  China Center for Disease Control and Prevention. Available online:
  https://www.chinacdc.cn/jkzt/crb/zl/szkb\_13037/gwjszl\_13092/
  (accessed on October 17, 2023).
\item
  Dou, X., Li, F., Ren, Z., Zhang, D., Li, J., Li, D., Sun, Y., Jin, H.,
  Li, R., Li, W. and Zhang, X., 2023. Clinical, Epidemiological, and
  Virological Features of Mpox in Beijing, China---May 31--June 21,
  2023.~\emph{Emerging Microbes \& Infections} , (just-accepted),
  p.2254407.
\item
  Du, Z., Shao, Z., Bai, Y., Wang, L., Herrera-Diestra, J.L., Fox, S.J.,
  Ertem, Z., Lau, E.H. and Cowling, B.J., 2022. Reproduction number of
  monkeypox in the early stage of the 2022 multi-country
  outbreak.~\emph{Journal of Travel Medicine} ,~\emph{29} (8),
  p.taac099.
\item
  Zhang, Y., Britton, T. and Zhou, X., 2022. Monitoring real-time
  transmission heterogeneity from incidence data.~\emph{PLOS
  Computational Biology} ,~\emph{18} (12), p.e1010078.
\item
  Lloyd-Smith, J.O., Schreiber, S.J., Kopp, P.E. and Getz, W.M., 2005.
  Superspreading and the effect of individual variation on disease
  emergence.~\emph{Nature} ,~\emph{438} (7066), pp.355-359.
\item
  Riopelle, J.C., Munster, V.J. and Port, J.R., 2022. Atypical and
  unique transmission of monkeypox virus during the 2022 outbreak: an
  overview of the current state of knowledge.~\emph{Viruses} ,~\emph{14}
  (9), p.2012.
\item
  Guo, Z., Zhao, S., Sun, S., He, D., Chong, K.C. and Yeoh, E.K., 2023.
  Estimation of the serial interval of monkeypox during the early
  outbreak in 2022.~\emph{Journal of Medical Virology} ,~\emph{95} (1),
  p.e28248.
\item
  Love, J., LaPrete, C.R., Sheets, T.R., Vega Yon, G.G., Thomas, A.,
  Samore, M.H., Keegan, L.T., Adler, F.R., Slayton, R.B., Spicknall,
  I.H. and Toth, D.J., 2023. Characterizing spatiotemporal variation in
  transmission heterogeneity during the 2022 mpox outbreak in the
  USA.~\emph{medRxiv} , pp.2023-05.
\item
  Nakoune, E., Lampaert, E., Ndjapou, S.G., Janssens, C., Zuniga, I.,
  Van Herp, M., Fongbia, J.P., Koyazegbe, T.D., Selekon, B., Komoyo,
  G.F. and Garba-Ouangole, S.M., 2017. A nosocomial outbreak of human
  monkeypox in the Central African Republic. In~\emph{Open forum
  infectious diseases} ~(Vol. 4, No. 4, p. ofx168). US: Oxford
  University Press.
\end{enumerate}

\selectlanguage{english}
\FloatBarrier
\end{document}

