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\begin{document}
\title{Simplified assessment of the evolution of the COVID-19 epidemic in the
state of Cear\selectlanguage{ngerman}á - Brazil\selectlanguage{english}}
\author[1]{Francisco H. C. Felix}%
\author[2]{Juvenia Fontenele}%
\affil[1]{Hospital Infantil Albert Sabin - HIAS}%
\affil[2]{Federal University of Ceará }%
\vspace{-1em}
\date{\today}
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\selectlanguage{english}
\begin{abstract}
The COVID-19 pandemic imposed a major challenge on all health systems on
the planet. At the regional level, the state of Cear\selectlanguage{ngerman}á (Brazil) differs
from other Brazilian regions by an early and rapid onset of its cases,
probably due to its high international connectivity by air. Health
authorities instituted social isolation measures 3 weeks ago. The
authors made a graphical inspection of official data on confirmed cases
of COVID-19 in Ceará, São Paulo, Brazil and the USA to search for
evidence that can help assess the strategy of local health authorities.
Logarithmic scale graphs of new cases per day and cumulative cases
indicate a high risk situation for the epidemic in Ceará. The tendency
for the pandemic to grow seems to be greater in Ceará than in the state
of São Paulo, in the whole of Brazil and even in the USA, the country
with the greatest growth of the epidemic recently. The maintenance and
even the tightening up of social isolation measures seem a logical
conclusion to this panorama.%
\end{abstract}\selectlanguage{ngerman}%
\sloppy
\section*{Introduction}
{\label{962180}}
On December 31, 2019, 27 cases of viral pneumonia were reported in the
city of Wuhan, China. A new coronavirus, related to SARS-Cov and
MERS-Cov, was isolated from the patients' airways, being initially named
2019-nCov~\cite{Zhu2020}. The sequence of events that followed gave
rise to the current pandemic of the new coronavirus, officially called
SARS-Cov-2~\cite{Bedford2020}. Mathematical models of spreading
SARS-Cov-2 indicate that screening and isolating cases and contacts is
not sufficient to contain the epidemic if there is a significant number
of asymptomatic patients transmitting the virus~\cite{Hellewell2020}.
Quarantine and social isolation measures can be effective for their
control, based on what happened in China~\cite{Anastassopoulou2020,Hou_2020}. In the
state of Cear\selectlanguage{ngerman}á, the first case was officially registered on March 15,
2020, five days after community transmission of the virus was declared
and, as of today (April 5), 823 confirmed cases have accumulated.
Quickly identifying the parameters of the COVID-19 epidemic is important
in deciding what appropriate measures to take. The authors have used a
simplified approach to graphical inspection of official data to date to
define what stage of the epidemic we are in our state and whether the
measures adopted have already changed the growth of cases.
\section*{Methods}\label{methods}
\subsection*{Data source:}\label{data-source}
The data were obtained from official sources. The number of confirmed
cases per day and the cumulative total in Ceará was obtained from the
Ceará State Government information site, IntegraSUS \cite{cear2020}.
The number of confirmed cases per day and the cumulative total in the
state of São Paulo was obtained from the coronavirus information site in
the state of São Paulo \cite{paulo}. The number of confirmed cases
per day and the cumulative total in Brazil and the USA was obtained from
the Worldometer \cite{worldometersinfo2020} website.
\subsection*{Statistical analysis:}\label{statistical-analysis}
The data were used to build a graph of evolution of the daily and
cumulative number of cases over time, between 03/15/2020 and 04/04/2020
(fig. 1). To provide support for a semi-quantitative assessment through
visual inspection of the graphs and comparison of metrics, we
constructed graphs plotting the number of new cases versus the total
cumulative number each day, both on a logarithmic scale (Fig. 2).
Using the least squares method, we performed a linear regression with
the data obtained, calculating the coefficient of determination
(\(R^2\)) as a surrogate metric to assess the departure of
the data from an ideal linear model. The program used was Google Sheets
(Google, 2020).
\section*{Results}\label{results}
The visual inspection of the graph of the number of confirmed cases over
time in two Brazilian states, in Brazil as a whole and in the United
States of America are similar, approaching a linear trend on a
logarithmic scale, which corresponds to a growth exponential on a linear
scale (figure 1). This suggests that all territories whose data have
been assessed are in the exponential phase of the COVID-19 epidemic, as
would be expected.
Visual inspection of the graphs of new cases versus cumulative cases on
a logarithmic scale is sensitive to small deviations from the linear
model, which indicate trends in the growth of the epidemic. Linear
regression and values of \(R^2\) also inform growth trends in
the evaluated populations.
The graphs of new cases versus cumulative cases visually show a most
pronounced departure from the linear trend in the case of the state of
Ceará, indicating a more explosive exponential trend. This deviation
appears to be even greater than in the case of the USA, which constitute
the territory with the highest number of cases and the fastest growing
epidemic on the planet (figure 2). The values of the coefficient of
determination are greater than 0.8 in the case of Brazil and the USA,
indicating a good correlation between the data and the model. In the
case of Ceará and São Paulo, the \(R^2\) is less than 0.7,
being closer to 0.6 in the case of our state. This indicates a smaller
correlation between the data and the model.
\subsection*{Suplement}\label{suplement}
This version is a translation from the
\href{https://www.authorea.com/users/78332/articles/439810-avalia\%C3\%A7\%C3\%A3o-gr\%C3\%A1fica-simplificada-da-evolu\%C3\%A7\%C3\%A3o-da-epidemia-covid-19-no-estado-do-cear\%C3\%A1?commit=765bf68b5cb0abf8a033657be6c785902ee8f790\#Bedford_2020}{original}
version in portuguese. Link: https://bit.ly/2XIL4vE
Data and graphs can be
\href{https://docs.google.com/spreadsheets/d/1Xtmm2tUF1qMJhXPO2QHplqrP0OpCbVa1tgVokCJpxOk/edit?usp=sharing}{visualized}
on google sheets: https://bit.ly/2VtKsaA
\section*{Discussion}\label{discussion}
This simplified assessment may suggest that the growing trend of the
COVID-19 epidemic has not yet been inhibited in Ceará, and that there is
less reliability in forecasts from the data in the case of our state.
One hypothesis that can be raised is that the epidemic is not controlled
in Ceará. Another hypothesis is that local data are incomplete or skewed
in some way (for example, by the recent change in the testing indication
for the virus).
The state of Ceará is one of the most affected in the Brazilian
territory by the COVID-19 pandemic. This is in contrast to other
neighboring states and the hypothesis that virus transmission is reduced
near the equator \cite{Sajadi_2020}. An analysis of air traffic data
estimated that air connectivity correlates positively with the spread of
COVID-19 \cite{De_Salazar_2020}. Fortaleza, capital of Ceará, has
considerably increased its air connectivity in recent years by
installing an air hub for Europe and expanding its air transport
operations \cite{castro2018}. This may be one of the most important
determining factors for the precocity of the COVID-19 epidemic in our
state. Three weeks ago, health authorities instituted measures to
contain the epidemic (quarantine, social isolation) in our state. There
is still no evaluation on the response to these measures.
Previous experience with the SARS pandemic \cite{Wallinga_2004} has shown
that the epidemic curve can be fundamentally different in different
affected regions even when connected geographically and temporally. It
also showed that the preparation and institution of adequate measures to
prevent and combat the epidemic are essential. Mathematical models have
shown that the current new pandemic of COVID-19 has the potential to
cause large numbers of deaths and collapse of health systems
\cite{Wu_2020}. A mathematical model recently developed by Brazilian
researchers showed a high risk of collapse of health resources in the
country and predicted that the measures currently underway (quarantine,
social isolation) need to be maintained for a longer time, or else the
effort may not have favorable result \cite{cajueiro2020}.
Our results from a simplified semi-quantitative assessment also indicate
that efforts to contain the pandemic in the state of Ceará need to
continue, as we are probably on the verge of entering the more
accelerated phase of the exponential curve of the epidemic. In addition,
there should be an increased effort to test and provide transparent
information on the evolution of the epidemic.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/cn-and-cc/cn-and-cc}
\caption{\selectlanguage{ngerman}{Daily new cases (cn - columns) and cumulative confirmed cases (cc -
lines) of COVID-19 in Ceará (blue), São Paulo (green), Brazil (orange)
and USA (red). Logarithmic scale.
{\label{428036}}%
}}
\end{center}
\end{figure}\selectlanguage{ngerman}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Blank-Diagram/Blank-Diagram}
\caption{\selectlanguage{ngerman}{Log scale graph of daily new cases (cn) versus cumulative cases (cc) and
linear regression trend using the least squares method. Cases on Ceará
(blue), São Paulo (green), Brazil (orange) and USA(red).~
{\label{497192}}%
}}
\end{center}
\end{figure}\selectlanguage{ngerman}
\selectlanguage{english}
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