**Simulated the Infectious Trend of COVID-19 in Selangor**

**by Using the SIR Model**

\*\*This is a Double-blind review, please do not include authors information in this version \*\*

Received Date: \*date

Accepted Date: \*date

Published Date: \*date

**HIGHLIGHTS**

  - Malaysian government took proactive measures and efficient strategies after recognizing the alarming trend of COVID-19.

  - The population of infected individuals in Selangor is estimated to predict the percentage of infection.

  - The SIR model aims to forecast the number of individuals susceptible to infection, actively infected, or recovered from the disease.

  - Basic reproduction provides an indication of concerning an outbreak.

ABSTRACT

*Coronavirus Disease 2019 (COVID-19) was initially reported in December 2019 in Wuhan City, China, as a result of a respiratory pandemic. Since then, the infection has spread rapidly and uncontrollably around the globe, prompting the World Health Organization (WHO) to declare it a pandemic. The study's overall objective is to imitate the COVID-19 infectious trend in Selangor. The SIR model is used to forecast infection and the course of COVID-19 diffusion and estimate the fraction of the population infected. As a result, the Susceptible, Infectious, and Recovered (SIR) model was used to accomplish the study's aims. From March 23, 2020, to June 30, 2020, 100 days of COVID-19 data were extracted from a database on the Malaysian Ministry of Health's website. The RStudio software was used to analyse data on infectious trends in this study. The SIR model is used to predict the basic reproduction ratio,* \(R_{0}\)*, based on actual and simulated infectious trends for comparison. The basic reproduction ratios for modelling the infectious trend with the entire population of Selangor are 1.15 and 2.0, respectively. According to the findings of this study, the reproduction ratio would affect the number of infected individuals by reducing the number of recovered individuals. The effectiveness of lockdown in preventing COVID-19 disease in Selangor was demonstrated by a significant reduction in the basic reproduction ratio,* \(R_{0}\)*.*

***Keywords:** SIR Model, COVID-19, Infectious Trend, Selangor, Reproduction Ratio*

# INTRODUCTION 

Coronavirus Disease (COVID-19) is a type of SARS-CoV-2 virus classified as a coronavirus associated with severe acute respiratory syndrome. SARS-CoV-2 is a zoonotic virus with striking genetic similarities to bat coronaviruses. It is associated with a bat-borne virus, implying that it evolved from a bat-borne virus. The name of COVID-19 is a short form from the word ‘CO” for corona, ‘VI’ for a virus, and ‘D’ for disease. Officials in Wuhan City, China, announced the first cases of COVID-19 in December 2019 as detected by a respiratory epidemic in China (Unicef, 2020). Since then, the epidemic's geographical expansion has been rapid and uncontrollable, resulting in the World Health Organization declaring it a pandemic (WHO). April 17, 2020, there are 2,230,439 positive cases of COVID-19 that have been reported worldwide, with total death 150,810 and a total recovered 564,210 (WHO, 2020).

COVID-19 has a variety of various effects on different persons. The majority of infected persons will experience mild to moderate symptoms and will heal on their own. Fever, dry cough, and tiredness are the most prevalent symptoms associated with COVID-19. Individuals must seek emergency medical treatment if they develop major symptoms such as breathing difficulty or shortness of breath, thorax or pressure, and voice or movement loss. COVID-19 was disseminated through direct contact with the infected individual's respiratory tract and coughing and sneezing. Individuals can potentially become infected by touching virus-infested surfaces and touching their faces (Unicef, 2020). 80% of those who were infected with the symptom were healed from the sickness without hospital treatment. Another 15% get severely unwell and need breathing care, while the other 5% get seriously ill and need treatment. (WHO, 2020) Imported cases of positive COVID-19 from China were by Health Minister Datuk Seri Dr. Dzulkefly Ahmad to the first COVID-19 wave between January 25, 2020, and February 26, 2020, through three instances involving three Chinese tourists entering Malaysia via Johor from Singapore on January 23, 2020 (New Straits Time, 2020). The first three cases involve Chinese nationals. They are in close proximity to a 66-year-old coronavirus patient who is being treated in Singapore and had been quarantined for many days in a Johor Bharu hotel. They were subsequently sent to Selangor's Sungai Buloh Hospital for additional treatment.

Malaysia's Ministry of Health and Government implemented a statewide 'Movement Control Order' (MCO). MCO is responsible for implementing new clusters on the specified site if the requisite number of cases occurs. Even the Ministry of Health's number of cases was uncertain, and residents believe MCO will help slow the COVID-19 outbreak in Selangor. Full lockdown in Selangor would jeopardise the country's economic recovery, and specialists believe that the rising number of Covid-19 infections must be contained. Given the circumstances in Selangor, economists feel that the long-term advantages outweigh the short-term costs. However, the trend of COVID-19 cases was unexpected, requiring various measures to deal with the pandemic and contain the epidemic in Selangor. As a result, using the Susceptible, Infectious, and Removed (SIR) mathematical model, researchers were able to recreate the COVID-19 epidemic's infectious trend in Selangor.

**METHODOLOGY**

The MCO implemented prohibitions against movements, international meetings, travel, and forced closures of enterprises, industries, governments, and education demands to control the spread of SARS-CoV-2, the virus that causes COVID-19 in Malaysia. As a result, secondary data were gathered for this study from a database available on the Ministry of Health Malaysia's website. There are 100 days of COVID-19 data collected from March 23, 2020, until June 30, 2020. The data consists of information such as the number of confirmed, recovered, death, and cumulative cases in Selangor (MOH, n.d.)

**Model Formulation**

In Fred Brauer's revisited paper, W. O. Kermack and A. G. McKendrick developed the mathematical model (SIR) in 1927, which considered a fixed population with three compartments. (Brauer, 2005). The model is intended for those who are susceptible, infectious, and have recovered. The SIR model is fairly realistic for infectious diseases that are transmitted from person to person and for which recovery confers long-term resistance. S, I, and R are variables that indicate the population size of each compartment at any particular time. To show that even if the total population size remains constant, the number of susceptible, infectious, and recovered individuals can change over time. Make the exact values S(t), I(t), and R(t) is a function of t (time). These functions were developed for a specific disease in a population to forecast probable outbreaks and put the disease under control.

Figure 1 shows the process of the mathematical model of the SIR model. The Susceptible, Infectious, and Removed are states in which an individual progresses in sequence.

Let *N* be the constancy of the population of individuals who live in Selangor in 2020.

*S(t) =* The number of susceptible individuals able to contact the disease.

*I(t) =* The number of infective individuals capable of transmitting the disease.

*R(t) =* The number of recovered individuals who have become immune.

*β =* transmission rate of disease.

\(\gamma =\) removal rate.

A set of ordinary differential equations may explain the evolution and dynamics of the SIR model as follows:

![fraction numerator d S over denominator d t end fraction equals negative fraction numerator beta I S over denominator N end fraction comma](630dd2be7b57e_media/media/image1.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mfrac\>\<mrow\>\<mi\>d\</mi\>\<mi\>S\</mi\>\</mrow\>\<mrow\>\<mi\>d\</mi\>\<mi\>t\</mi\>\</mrow\>\</mfrac\>\<mo\>=\</mo\>\<mo\>-\</mo\>\<mfrac\>\<mrow\>\<mi\>β\</mi\>\<mi\>I\</mi\>\<mi\>S\</mi\>\</mrow\>\<mi\>N\</mi\>\</mfrac\>\<mo\>,\</mo\>\</mstyle\>\</math\>\"}") (3.1)

![fraction numerator d I over denominator d t end fraction equals fraction numerator beta I S over denominator N end fraction minus gamma I comma](630dd2be7b57e_media/media/image2.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mfrac\>\<mrow\>\<mi\>d\</mi\>\<mi\>I\</mi\>\</mrow\>\<mrow\>\<mi\>d\</mi\>\<mi\>t\</mi\>\</mrow\>\</mfrac\>\<mo\>=\</mo\>\<mfrac\>\<mrow\>\<mi\>β\</mi\>\<mi\>I\</mi\>\<mi\>S\</mi\>\</mrow\>\<mi\>N\</mi\>\</mfrac\>\<mo\>-\</mo\>\<mi\>γ\</mi\>\<mi\>I\</mi\>\<mo\>,\</mo\>\</mstyle\>\</math\>\"}") (3.2)

![fraction numerator d R over denominator d t end fraction equals gamma I comma](630dd2be7b57e_media/media/image3.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mfrac\>\<mrow\>\<mi\>d\</mi\>\<mi\>R\</mi\>\</mrow\>\<mrow\>\<mi\>d\</mi\>\<mi\>t\</mi\>\</mrow\>\</mfrac\>\<mo\>=\</mo\>\<mi\>γ\</mi\>\<mi\>I\</mi\>\<mo\>,\</mo\>\</mstyle\>\</math\>\"}") (3.3)

where S, I, and R represent, the susceptible, infected, and recovered total number of individuals representing each compartment. *N* is the total population size.

Since,

![fraction numerator d S over denominator d t end fraction plus fraction numerator d I over denominator d t end fraction plus fraction numerator d R over denominator d t end fraction equals 0](630dd2be7b57e_media/media/image4.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mfrac\>\<mrow\>\<mi\>d\</mi\>\<mi\>S\</mi\>\</mrow\>\<mrow\>\<mi\>d\</mi\>\<mi\>t\</mi\>\</mrow\>\</mfrac\>\<mo\>+\</mo\>\<mfrac\>\<mrow\>\<mi\>d\</mi\>\<mi\>I\</mi\>\</mrow\>\<mrow\>\<mi\>d\</mi\>\<mi\>t\</mi\>\</mrow\>\</mfrac\>\<mo\>+\</mo\>\<mfrac\>\<mrow\>\<mi\>d\</mi\>\<mi\>R\</mi\>\</mrow\>\<mrow\>\<mi\>d\</mi\>\<mi\>t\</mi\>\</mrow\>\</mfrac\>\<mo\>=\</mo\>\<mn\>0\</mn\>\</mstyle\>\</math\>\"}") (3.5)

Follows that,

![N equals S open parentheses t close parentheses plus I open parentheses t close parentheses plus R open parentheses t close parentheses](630dd2be7b57e_media/media/image5.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>N\</mi\>\<mo\>=\</mo\>\<mi\>S\</mi\>\<mfenced\>\<mi\>t\</mi\>\</mfenced\>\<mo\>+\</mo\>\<mi\>I\</mi\>\<mfenced\>\<mi\>t\</mi\>\</mfenced\>\<mo\>+\</mo\>\<mi\>R\</mi\>\<mfenced\>\<mi\>t\</mi\>\</mfenced\>\</mstyle\>\</math\>\"}"),*N=constant* (3.6)

The dynamics of the infectious class depends on the following ratio,

![R subscript 0 equals beta over gamma comma](630dd2be7b57e_media/media/image6.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\>=\</mo\>\<mfrac\>\<mi\>β\</mi\>\<mi\>γ\</mi\>\</mfrac\>\<mo\>,\</mo\>\</mstyle\>\</math\>\"}") (3.7)

It’s called a basic reproduction ratio. This ratio is derived as the expected number of new infections or called as secondary infections from a single infection in a population. \(R_{0}\text{\ \ }\)indicate the severity of the outbreak of an infectious disease of COVID-19.

If the value of reproduction ratio is,

![R subscript 0 less than 1](630dd2be7b57e_media/media/image7.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\>&lt;\</mo\>\<mn\>1\</mn\>\</mstyle\>\</math\>\"}"), (3.8)

Each infected individual will only infect one other individual, and the disease will eventually die out.

![R subscript 0 equals 1](630dd2be7b57e_media/media/image8.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\>=\</mo\>\<mn\>1\</mn\>\</mstyle\>\</math\>\"}"), (3.9)

Each infected individual will infect one more individual, and the disease will continue to spread yet remain stable.

![R subscript 0 greater than 1](630dd2be7b57e_media/media/image9.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\>&gt;\</mo\>\<mn\>1\</mn\>\</mstyle\>\</math\>\"}"), (3.10)

Each infected individual will infect other individuals, and the disease will continue to spread and expand, with the potential to become a pandemic.

**Numerical Solution**

A numerical simulation of the infectious trend of COVID-19 in Selangor was conducted to analyse the infection and course of COVID-19 spread. The SIR model forecasts the future dynamics of epidemics simulated by the SIR model using Microsoft Excel to extract parameters from collected data and R-software to solve the SIR model numerically. The basic reproduction ratio ![R subscript 0](630dd2be7b57e_media/media/image10.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\</mstyle\>\</math\>\"}") , provides \(S\) indications concerning an outbreak:

1.  > Whether or not the outbreak will evolve into a pandemic scale.

2.  > The epidemic's initial rate of spread.

3.  > The proportion of the susceptible population that will get infected in the end.

4.  > In a population, the equilibrium fraction of susceptible individuals.

**FINDINGS AND DISCUSSIONS**

**Solutions of The SIR Model**

The chart in **Figure 2** illustrates the total number of new cases, total number of recovered cases, and total number of mortality cases of COVID-19 in Selangor every week. In this work, this data was used to mimic the infectious trend using the SIR model.

> <span class="chart">\[CHART\]</span>

**Figure 2:** The difference of total new cases, recovered cases, and death cases of COVID-19 in Selangor per week

To find the solution for COVID-19 cases in Selangor, the value of the parameters \(\beta\)*,* \(\gamma\)*,* and \(\mu\) that calculated based on **Table 1**. For the initial condition, the value of parameters was then substituted into Eq (3.1) until Eq (3.3). **Table 1** depicts the initial condition values for instances of COVID-19 in Selangor, as determined by the starting condition. Estimates of the fundamental reproduction number ![R subscript 0](630dd2be7b57e_media/media/image11.png) are shown in **Table 2**. From March 24, 2020, to March 26, 2020, the transmission rate (![beta](630dd2be7b57e_media/media/image12.png)) and the removal / recovery rate (![gamma](630dd2be7b57e_media/media/image13.png)) were measured.

Table 1: The values of parameters for COVID-19 cases in Selangor

| *Parameters*        | *COVID-19 in Selangor* |
| ------------------- | ---------------------- |
| \[\mathbf{N}\]      | *6520000*              |
| \[\mathbf{\beta}\]  | *1.29076*              |
| \[\mathbf{\gamma}\] | *0.62963*              |

**Table 2:** Initial condition’s values for cases of COVID-19 in Selangor.

| *Initial Condition*                                                                                                                                                                                                                                                                                                 | *COVID-19 in Selangor* |
| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------- |
| ![S open parentheses 0 close parentheses](630dd2be7b57e_media/media/image14.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>S\</mi\>\<mfenced\>\<mn\>0\</mn\>\</mfenced\>\</mstyle\>\</math\>\"}") | *0.99993*              |
| ![I open parentheses 0 close parentheses](630dd2be7b57e_media/media/image15.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>I\</mi\>\<mfenced\>\<mn\>0\</mn\>\</mfenced\>\</mstyle\>\</math\>\"}") | 5.7515E-05             |
| ![R open parentheses 0 close parentheses](630dd2be7b57e_media/media/image16.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>R\</mi\>\<mfenced\>\<mn\>0\</mn\>\</mfenced\>\</mstyle\>\</math\>\"}") | 0                      |

**Table 3:** Basic reproduction number (![R subscript 0](630dd2be7b57e_media/media/image10.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\</mstyle\>\</math\>\"}")). transmission rate (β) and removed  
/ recovery rate (γ).

| *Date*                       | ![R subscript 0](630dd2be7b57e_media/media/image10.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\</mstyle\>\</math\>\"}") | ![beta](630dd2be7b57e_media/media/image17.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>β\</mi\>\</mstyle\>\</math\>\"}") | ![gamma](630dd2be7b57e_media/media/image18.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>γ\</mi\>\</mstyle\>\</math\>\"}") |
| ---------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| *24<sup>th</sup> March 2020* | *2.05003*                                                                                                                                                                                                                                                                            | *1.29076*                                                                                                                                                                                                                                    | *0.69263*                                                                                                                                                                                                                                     |
| *25<sup>th</sup> March 2020* | *1.21778*                                                                                                                                                                                                                                                                            | *0.13786*                                                                                                                                                                                                                                    | *0.11321*                                                                                                                                                                                                                                     |
| *26<sup>th</sup> March 2020* | *2.50083*                                                                                                                                                                                                                                                                            | *0.16239*                                                                                                                                                                                                                                    | *0.66667*                                                                                                                                                                                                                                     |

*The data of covid cases for the infectious trend that has been simulated by days is represented on the x-axis of the graph. The y-axis, on the other hand, depicts the prevalence of COVID-19 cases in Selangor in 2020.*

![Chart, line chart Description automatically generated](630dd2be7b57e_media/media/image19.png)

**Figure 3:** The SIR model for COVID-19 cases in Selangor

**Figure 3** illustrates the graph for COVID-19 cases in Selangor using the SIR model. The red line represents the simulated number of susceptible individuals, the green line represents the simulated number of infected individuals, and the blue line represents the simulated number of recovered numbers of infected individuals. This graph covered a period of 100 days. The results indicate that the number of probable sick individuals in the red line fell by 37 days. Within 63 days, the number of infected persons depicted by the green line begins to rise and reaches a peak of 0.13 prevalence. Meanwhile, the blue line depicting the number of people who recovered from various diseases reaches 0.82 prevalence, the largest number of afflicted people in Selangor in 87 days. After 93 days, the disease has stopped spreading, implying that it only spread for 67 days.

The SIR model is initialized (at the time ![t space equals space 0](630dd2be7b57e_media/media/image20.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>t\</mi\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mn\>0\</mn\>\</mstyle\>\</math\>\"}")) using the total population, ![N space equals space 6520000](630dd2be7b57e_media/media/image21.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>N\</mi\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mn\>6520000\</mn\>\</mstyle\>\</math\>\"}") with the initial condition ![S open parentheses 0 close parentheses equals S subscript 0 space end subscript equals 6513480](630dd2be7b57e_media/media/image22.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>S\</mi\>\<mfenced\>\<mn\>0\</mn\>\</mfenced\>\<mo\>=\</mo\>\<msub\>\<mi\>S\</mi\>\<mrow\>\<mn\>0\</mn\>\<mo\> \</mo\>\</mrow\>\</msub\>\<mo\>=\</mo\>\<mn\>6513480\</mn\>\</mstyle\>\</math\>\"}") (99.9% from the total population), and ![I open parentheses 0 close parentheses space equals space I subscript 0 space equals space 6520](630dd2be7b57e_media/media/image23.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>I\</mi\>\<mfenced\>\<mn\>0\</mn\>\</mfenced\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<msub\>\<mi\>I\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mn\>6520\</mn\>\</mstyle\>\</math\>\"}") (0.1% from the total population). The basic reproductive number ![R subscript 0](630dd2be7b57e_media/media/image10.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\</mstyle\>\</math\>\"}") for this study uses the average ![R subscript 0 equals 1.154292396 space](630dd2be7b57e_media/media/image24.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\>=\</mo\>\<mn\>1\</mn\>\<mo\>.\</mo\>\<mn\>154292396\</mn\>\<mo\> \</mo\>\</mstyle\>\</math\>\"}")from the calculation in excel (Refer Appendix D). The average recorded number of days of recovery is to be 3 days based on the selected recovered cases in Selangor. It follows the recovery cases rate ![gamma space equals space O.368](630dd2be7b57e_media/media/image25.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>γ\</mi\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mi\>O\</mi\>\<mo\>.\</mo\>\<mn\>368\</mn\>\</mstyle\>\</math\>\"}") and the value of transmission rate ![beta equals 0.425](630dd2be7b57e_media/media/image26.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>β\</mi\>\<mo\>=\</mo\>\<mn\>0\</mn\>\<mo\>.\</mo\>\<mn\>425\</mn\>\</mstyle\>\</math\>\"}"). Finally, with the values of ![S subscript 0 comma space I subscript 0 comma](630dd2be7b57e_media/media/image27.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>S\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\>,\</mo\>\<mo\> \</mo\>\<msub\>\<mi\>I\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\>,\</mo\>\</mstyle\>\</math\>\"}")and ![R subscript 0](630dd2be7b57e_media/media/image10.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\</mstyle\>\</math\>\"}") the differential equations were solved the values compartments at each time point (days) beginning from day zero (March 23, 2020) until day 100 (June 30, 2020). As a result of Eq. (3.7)

![R subscript O space equals space beta over gamma space space space space space space space equals space fraction numerator 0.42548 over denominator 0.36861 end fraction space space space space space space space equals space 1.15429](630dd2be7b57e_media/media/image28.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mi\>O\</mi\>\</msub\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mfrac\>\<mi\>β\</mi\>\<mi\>γ\</mi\>\</mfrac\>\<mspace linebreak=\\\"newline\\\"/\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mfrac\>\<mrow\>\<mn\>0\</mn\>\<mo\>.\</mo\>\<mn\>42548\</mn\>\</mrow\>\<mrow\>\<mn\>0\</mn\>\<mo\>.\</mo\>\<mn\>36861\</mn\>\</mrow\>\</mfrac\>\<mspace linebreak=\\\"newline\\\"/\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mn\>1\</mn\>\<mo\>.\</mo\>\<mn\>15429\</mn\>\</mstyle\>\</math\>\"}")

For the simulated infectious trend with the same total population, *N* and the initial condition of ![S open parentheses 0 close parentheses](630dd2be7b57e_media/media/image14.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>S\</mi\>\<mfenced\>\<mn\>0\</mn\>\</mfenced\>\</mstyle\>\</math\>\"}")and ![I open parentheses 0 close parentheses](630dd2be7b57e_media/media/image15.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>I\</mi\>\<mfenced\>\<mn\>0\</mn\>\</mfenced\>\</mstyle\>\</math\>\"}")were used. The parameter of beta and gamma were assumed as the recovery cases rate, ![beta space equals space 0.50](630dd2be7b57e_media/media/image29.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>β\</mi\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mn\>0\</mn\>\<mo\>.\</mo\>\<mn\>50\</mn\>\</mstyle\>\</math\>\"}"), the value of transmission rate, ![gamma space equals space 0.25](630dd2be7b57e_media/media/image30.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>γ\</mi\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mn\>0\</mn\>\<mo\>.\</mo\>\<mn\>25\</mn\>\</mstyle\>\</math\>\"}"), and the average of recovery is assumed to be 4 days for recovered cases in Selangor. Then, the reproductive number, Ro for this simulation using the formula below. Eq (3.7) gives the following information:

![R subscript 0 space equals space beta over gamma space space space space space space equals space fraction numerator 0.50000 over denominator 0.25000 end fraction space space space space space space equals space 2.00000](630dd2be7b57e_media/media/image31.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mfrac\>\<mi\>β\</mi\>\<mi\>γ\</mi\>\</mfrac\>\<mspace linebreak=\\\"newline\\\"/\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mfrac\>\<mrow\>\<mn\>0\</mn\>\<mo\>.\</mo\>\<mn\>50000\</mn\>\</mrow\>\<mrow\>\<mn\>0\</mn\>\<mo\>.\</mo\>\<mn\>25000\</mn\>\</mrow\>\</mfrac\>\<mspace linebreak=\\\"newline\\\"/\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mn\>2\</mn\>\<mo\>.\</mo\>\<mn\>00000\</mn\>\</mstyle\>\</math\>\"}")

![Chart, histogram Description automatically generated](630dd2be7b57e_media/media/image32.png)

**Figure 4:** The actual infectious trend for 100 days

**Figure 4** shows the graphs of the actual infectious trend of COVID-19 in Selangor for 100 days. The *x-axis* represents the duration of time in days, and the *y-axis* represents the total number of infected individuals with coronavirus diseases. In the initial stage, day zero to day 12 (April 4, 2020), the actual trend reach a peak value of more than 1000000 individuals on day 20 to 24, and going downwards after day 25 (April 17, 2020), the simulation remains constant after day 50 until after day 100 (June 30, 2020).

![Chart, line chart Description automatically generated](630dd2be7b57e_media/media/image33.png)

**Figure 5:** The simulated infectious trend for 100 days

**Figure 5** illustrates the trend of simulated COVID-19 infection in Selangor over a 100-day period. The x-axis indicates the duration of the disease in days, while the y-axis indicates the total number of persons affected by it. The simulation remains consistent from day 0 to day 25 during the early period. From day 38, the simulation trended upward, reaching a peak of 1000000 persons on day 62. (May 22, 2020). The simulated trend continues to decline after day 64, almost approaching zero on day 94.

![Chart, line chart Description automatically generated](630dd2be7b57e_media/media/image34.png)

**Figure 6:** The reproduction number level for actual infectious trend

**Figures 6** represents the graphs of reproduction number levels for actual infectious trend with the parameters of ![beta space equals space 1.29076](630dd2be7b57e_media/media/image35.png) and ![gamma space equals space 0.62963](630dd2be7b57e_media/media/image36.png). Based on the result, the green line shows that the reproduction number starts to decline from day 13 and reaches zero after day 31.

![Chart, line chart Description automatically generated](630dd2be7b57e_media/media/image37.png)

**Figure 7:** The reproduction number level for simulated infectious trend

**Figures 7** show graphs of reproduction number levels for a simulated infectious trend with the parameters ![beta space equals space 0.50000](630dd2be7b57e_media/media/image38.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>β\</mi\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mn\>0\</mn\>\<mo\>.\</mo\>\<mn\>50000\</mn\>\</mstyle\>\</math\>\"}") and ![gamma space equals space 0.25000](630dd2be7b57e_media/media/image39.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<mi\>γ\</mi\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mn\>0\</mn\>\<mo\>.\</mo\>\<mn\>25000\</mn\>\</mstyle\>\</math\>\"}"). According to the results, the green line indicates that the reproduction number begins to decline on day 43 and reaches one on day 75.

The reproduction number, ![R subscript 0 space equals space beta over gamma](630dd2be7b57e_media/media/image40.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\<mo\> \</mo\>\<mo\>=\</mo\>\<mo\> \</mo\>\<mfrac\>\<mi\>β\</mi\>\<mi\>γ\</mi\>\</mfrac\>\</mstyle\>\</math\>\"}"), is the product of the ratio of *β* and *γ* in Equation (3.7). The basic reproduction ratio for actual infectious trend is 1.15429, while the value of basic reproduction ratio for simulated infectious trend is 2.00000. This showed that the reproduction ratio of the simulated infectious trend was higher than the actual infectious trend. Since the value of ![R subscript 0](630dd2be7b57e_media/media/image10.png "{\"mathml\":\"\<math style=\\\"font-family:stix;font-size:16px;\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\>\<mstyle mathsize=\\\"16px\\\"\>\<msub\>\<mi\>R\</mi\>\<mn\>0\</mn\>\</msub\>\</mstyle\>\</math\>\"}") for both infectious trends is greater than 1, each infected individual will infect other individuals, and the disease will continue to spread and expand with the potential to become a pandemic.

**CONCLUSIONS AND RECOMMENDATIONS**

In this analysis, the whole population of Selangor is chosen as the constant population. At any point in time, the SIR model attempts to forecast the number of individuals who are susceptible to infection, actively infected, and recovered from disease. We can deduce an indication of the severity of the COVID-19 infectious disease outbreak based on the value of the reproduction ratio model, \(R_{0}\). The entire simulation illustrates the various reproduction ratio findings for both the actual and simulated infectious trends of COVID-19. Because of the reproduction ratio, each infected individual will infect others, causing the disease to spread and expand, potentially becoming a pandemic, as shown. This objective highlighted the importance of this study as a part of a larger piece of research in which future in-depth research on COVID-19 can be done. As a result, additional research should be conducted to replicate the SIR model using a logistic growth model for the population N value. Finally, incorporating the Exposed (E) component into the modelling technique by extending the current SIR model to the SEIR model appears to be a natural extension of this work's current research.

**ACKNOWLEDGEMENTS**

Alhamdulillah, praise and thank Allah because of His Almighty and His utmost blessings, I was able to complete this report on Simulated the Infectious Trend of COVID-19 in Selangor by Using the SIR Model. A special thanks go to my supervisor, who is giving me full responsibility, much idea and guiding me patiently from the first step of completing this research until the end of the semester. Special appreciation also goes to my beloved parents their support and encouraging me to finish this report.

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