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\begin{document}

\title{Susceptible-Infectious-Recovered (SIR) model based forecasting of
COVID-19 outbreak in Bangladesh}



\author[1]{Ashis Talukder}%
\affil[1]{Khulna University}%


\vspace{-1em}



  
  \date{May 20, 2024}


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\begin{abstract}
The 2019--20 coronavirus (COVID-19) pandemic was affirmed to have spread
to Bangladesh on March 2020. The initial three known cases were
accounted for by the nation's Institute of Epidemiology, Disease Control
and Research (IEDCR) on 7 March 2020. As of 15th April 2020, the
Government of Bangladesh has reported that there is a total of 1,231
confirmed cases, 49 recoveries, and 50 deaths in the whole country. In
this research, I try to forecast the COVID-19 outbreak in Bangladesh by
using a well-known epidemiological model,
Susceptible-Infectious-Recovered (SIR) model.%
\end{abstract}%



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\textbf{Title Page}

\textbf{Susceptible-Infectious-Recovered (SIR) model based forecasting
of COVID-19 outbreak in Bangladesh}

\textbf{Running Head: COVID-19 outbreak in Bangladesh}

\textbf{Ashis Talukder\textsuperscript{1}*}

\textsuperscript{1} Statistics Discipline, Khulna University,
Khulna-9208, Bangladesh.

\textsuperscript{\textbf{*}}\textbf{Corresponding Author:} Ashis
Talukder;\textbf{E-mail address:} ashistalukder27@yahoo.com

\textbf{Detailed Address of Corresponding Author:}

Ashis Talukder

Assistant Professor

Statistics Discipline

Khulna University, Khulna-9208, Bangladesh

E-mail:\emph{ashistalukder27@yahoo.com}

Contact no.: +8801772063507

\textbf{Susceptible-Infectious-Recovered (SIR) model based forecasting
of COVID-19 outbreak in Bangladesh}

The 2019--20 coronavirus (COVID-19) pandemic was affirmed to have spread
to Bangladesh on March 2020. The initial three known cases were
accounted for by the nation's Institute of Epidemiology, Disease Control
and Research (IEDCR) on 7 March 2020 {[}1{]}. As of
15\textsuperscript{th} April 2020, the~Government of Bangladesh~has
reported that there is a total of 1,231 confirmed cases, 49 recoveries,
and 50 deaths in the whole country {[}2{]}. In this research, I try to
forecast the COVID-19 outbreak in Bangladesh by using a well-known
epidemiological model, Susceptible-Infectious-Recovered (SIR) model.

The SIR model consists of three compartments: S stands for susceptible,
I stands for infectious, and R stands for recovered or deceased (or
immune) or removed individuals. This model has two parameters
\(\beta\)and \(\gamma\) which represents the infectious
contact rate and the recovery rate, respectively. Another key component,
the basic reproductive ratio \((R_{0})\) can be predicted with
the help of\(\beta\) and \selectlanguage{greek}γ. \selectlanguage{english}For details about
SIR model, see {[}3{]}.

To estimate the parameters I considered the everyday cases of the
COVID-19 over the period of March 7, 2020 to April 14, 2020 from
worldometers records {[}4{]}. The parameter estimates are displayed in
Table 1. From this Table, it is observed that the COVID-19 can be
transmitted through exposure in Bangladesh with a rate
of\(\ \beta=0.0014\). The value of \(\gamma\) is found to be
0.2366 represents that the disease can be recovered in a specific period
at a rate of 0.2366. Moreover, the average number of people infected
from one other person is more than 7 (\(R_{0}=7.14\)).

Now, I try to draw the SIR model curve by utilizing the estimated values
of \selectlanguage{greek}β \selectlanguage{english}and \selectlanguage{greek}γ \selectlanguage{english}with some additional information of susceptible, infectious
as well as recovered individuals at initial stage. As of April 14, 2020
the IEDCR informed that among 1,905 tested samples there are 209
confirmed cases with no recovered individuals {[}2{]}. Note that, I want
to forecast the outbreak from April 15, 2020 to the next 30 days.
Therefore, at initial stage (April 14, 2020), the number of susceptible,
infectious and recovered individuals were 1,905, 209 and 0,
respectively. By utilizing all these information, the SIR curve had been
drawn. The curve is shown in Figure 1. Basically, the figure illustrate
how the number of each component (S, I and R) can be changed over time,
according to the SIR model.

In Figure 1 the X-axis represents the time periods, specifically the
number of days since the beginning of the outbreak. The Y-axis
represents the number of people in each of three categories in each day.
Note that, in X-axis the 0 value represents the April 14, 2020 since I
want to forecast the outbreak from April 15, 2020. The red, green and
blue color represents the susceptible, infectious and recovered
individuals, respectively.

The quick decline of the red line (the number of people who have not
been yet been infected) indicates that the disease is very contagious,
with almost every susceptible individuals being infected by the
5\textsuperscript{th} day from starting point (i.e April 20, 2020). The
green line (the daily number of infected cases) changes rapidly up to
maximum by the 3\textsuperscript{rd} day and then falls more slowly
until about 25\textsuperscript{th} day when nearly everyone has
recovered. Finally, the blue line (the number of recovered cases)
increases steadily and reaches the highest point at the
21\textsuperscript{st} day, indicating almost everyone will be recovered
from disease. Note that, in the whole course of action, death may be
occurred and SIR model consider these death into recovered cases.

Finally, it should be bear in mind that this is a model based
forecasting of the outbreak and the estimates are calculated from
available information. If several protective measures will not be taken,
then this rate may exist. However, the government of Bangladesh has
already taken various protective measures such as lockdown several
areas, facilitate quarantine etc. to reduce the rate of COVID-19
outbreak. Hopefully, our country will be successful to reduce the rate
of this outbreak.

\textbf{Funding Information}

No fund has been received

\textbf{Declaration of competing interest}

The author has no conflict of interest to disclosure

\textbf{References}

\begin{enumerate}
\tightlist
\item
  Bangladesh confirms its first three cases of coronavirus. Reuters. 8
  March 2020. Retrieved 27 March 2020.
\item
  Institute of Epidemiology, Disease Control and Research (IEDCR).
  Official website: https://www.iedcr.gov.bd/
\item
  Cant\selectlanguage{ngerman}ó, B., Coll, C. \& Sánchez, E. Estimation of parameters in a
  structured SIR model. Adv Differ Equ 2017, 33 (2017).
  https://doi.org/10.1186/s13662-017-1078-5
\item
  Worldometer. Available on: https://www.worldometers.info/coronavirus/
\end{enumerate}

\textbf{Hosted file}

\verb`Table.docx`  available at \url{https://authorea.com/users/311749/articles/442436-susceptible-infectious-recovered-sir-model-based-forecasting-of-covid-19-outbreak-in-bangladesh}\selectlanguage{english}
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