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Application of Mathematical Concepts

Contents

Introduction.

Assumption and Considerations

Methodology.

Results

Discussion and Evaluation.

Conclusion and Recommendation.

References.

Introduction to Belgium Coronavirus Analysis

A worldwide pandemic coronavirus (COVID-2019) has encompassed the whole world and Belgium is also hit by this lethal virus. Coronavirus is caused by severe acute respiratory syndrome (SARS-CoV-2). This virus was started spreading in Belgium on 4 February 2020 ("Belgium: new coronavirus cases October 3, 2020 | Statista", 2020). This virus was stated spreading rapidly in March-April 2020. In the March end, all ten provinces of country had 61,007 confirmed cases of coronavirus with total deaths 9,726. It is expected that actual number of cases will be higher than this figure because the laboratory test were for those people who had sever symptoms. Many people with acute or minor symptoms did not seek medical help but these people might responsible for transmitting virus too ("Belgium Coronavirus: 143,596 Cases and 10,126 Deaths - Worldometer", 2020)

The main purpose of the PSMT is solving the issue and modelling the situation observed the best model for the daily amount of COVID – 19 infection numbers and forecast the number of days. It will enforce the entire population to be affected if there is no action had been taken to combat the infection. This can be illustrated through application of mathematical concepts such as cumulative frequency and graph through using mathematical technology such as R² values and technology such as Demos and Excel.

Assumption and Considerations

Observations

1. Because the infection of the whole Belgian population have been taken into account without any intervention against the coronavirus. Thus, data from the first case up to the date before the limitations are enforced must be considered. However, there is not enough details available to perform an investigation. An unambiguous trend to establish an acceptable pattern cannot be generated by limited data. Cases remain at the first two weeks, and restrictions are made on March 19th , there are 1541 cases when restrictions were implemented. For an exact solution, more data will be required at this point.
2. This data is received from Worldometer, a reliable statistics website.

Assumptions

1. Based on the reports, the data only the diagnosed cases of infection and not all the cases of coronavirus. The restriction have been imposed by Belgium since March 19th, that is, about 28 days after the discovery of the first corona infection. Although, symptoms may not appear for up to two weeks, so people who are infected are not may not be able to perform testing right away. There are variety reasons why cases were low during the beginning of pandemic – due to people have not confirmed the seriousness of the virus, therefore refuse to test, medical lack of kits and asymptomatic cases. Thus, it would be appropriate to consider data values after two weeks, until March 31
2. It is believed that number of actual cases would be more than registered cases because people with mild symptoms did not seek medical advice.

Methodology

A variety of method will be created to enhance the solution. This will include:

• Data and collecting:

Reliable sources from World Health Organisation on the number of cases of the COVID – 19.

• The mathematical technology such as Excel will be required to indicate a modelled graph for the cumulative table and graph. Numerous types of function will be determined to compared and given which is the best and suitable for the graph.
• Modelling the cases:

The technology will be needed and used to create a trendline. R² closet to 1 should be reflected the most suitable for the graph.

• Solve the equation in the graph:

The formula of the trendline in the graph by using Demos to demonstrate how long it will take Belgium entire population given that x is the number of days and y is the number of cases.

Results

Table 1: Cumulative cases

 Day Daily cases Cumulative cases 1 18 18 2 19 37 3 34 71 4 53 124 5 81 205 6 110 315 7 27 342 8 65 407 9 94 501 10 99 600 11 174 774 12 250 1024 13 338 1362 14 179 1541 15 214 1755 16 387 2142 17 422 2564 18 534 3098 19 713 3811 20 663 4474 21 470 4944 22 486 5430 23 1328 6758 24 1195 7953 25 1199 9152 26 1363 10515 27 1519 12034

Example: Initial

As it can be seen in the data, to indicate which shape of the data best suits the chart such as exponential and quadratic trendline prediction. It can be seen clearly that the exponential shape is clearly the most suitable. The trend line of the coronavirus is at first at its lowest level, gradually increasing slowly, then accelerating to the highest level. The data demonstrates that the exponential model is a more preferable way of performing data. The R² value, a statistical measure of accuracy, and another indicator of which model is best suited for the data. The R² values for the exponential model - 0.9854 are almost less than 1, and both blue trend lines come together to generate an accurate exponential pattern. For testing the authenticity of the exponential model utilised in Excel and to forecast when the entire Belgian population would be infected, an exponential model was developed in the most automatic way.

Discussion and Evaluation on Belgium Coronavirus Analysis

‘R’ is called correlation coefficient. It is also known as coefficient of determination. R-Squared is a square of correlation coefficient. The value of R-squared is between 0 and 1 which implies as percentages between 0% and 100% respectively. If the value of R-Squared is 100% it means that dependent variable is completely explained by independent variable. The value of R-Squared tells that how good a data fits the regression line. A value of ‘1’ means that all the data fits the regression line while a value of ‘0’ means that no data fits the regression line ("How to Find R-Squared in Excel? Use (RSQ) Function", 2020).

The given data shows that the Corona cases in Belgium increase with the passage of time. Different trend lines are used to predict the cumulative Corona cases in Belgium. These trend lines are

• Linear
• Cubic
• Exponential

The linear trend line equation is

y= mx + c

Where,

‘Y’ is dependent variable

‘X’ is independent variable

‘m’ is slope

‘C’ is constant

An exponential equation takes the form

y= M1emx

The data that best fits the graph is cubic trend line.

Conclusion and Recommendation on Belgium Coronavirus Analysis

Belgium is included in the list of those countries which is badly impacted by coronavirus epidemic. Total 230 new cases were registered in country on 3rd October 2020. Total number of registered cases in Belgium has exceeded 130,000 till 3rd October, 2020. The area that is most affected by virus is Flanders but Flanders is densely populated as compared to other parts of Belgium.

The first death occurred in Belgium on 11th March. The number of cases has been increasing gradually and the current death toll is 10,001. The death rate in Belgium was 8.66% on September 29, 2020. The virus is affecting elder people more as compared to younger people and children.

The main purpose of the PSMT is solving the issue and modelling the situation observed the best model for the daily amount of COVID – 19 infection numbers and forecast the number of days. Data is collected from World Health Organisation on the number of cases of the COVID – 19.The mathematical technology such as Excel will be required to indicate a modelled graph for the cumulative table and graph. Numerous types of function will be determined to compare and given which is the best and suitable for the graph. The technology will be needed and used to create a trendline. R² close to 1 should be reflected the most suitable for the graph. The formula of the trendline in the graph by using Demos to demonstrate how long it will take Belgium entire population given that x is the number of days and y is the number of cases.

The graph shows that a cubic trend line best fit graph. The value of ‘R2’ is 0.9986 which implies that 99.86% of the data fits the regression line.

Currently, there is no vaccine to prevent corona virus. Corona virus can be prevented by adopting suitable precautions. These precautions are

• Wash your hands with soap for 20 seconds or use an alcohol based sanitizer to clean your hands
• Avoid crowded places
• Seek medical advice if you have fever, coughing or difficulty in breathing
• Maintain a safe distance (1-3 m) from people you are meeting
• Wear a face mask in public places
• Do not touch your mouth, face and eyes
• Bent your elbow on your mouth or nose while coughing or sneezing
• Disinfect your door handles, sink, tables, switches, sinks etc.
• Do not eat unhygienic food

References for Belgium Coronavirus Analysis

Belgium Coronavirus: 143,596 Cases and 10,126 Deaths - Worldometer. (2020). Retrieved 9 October 2020, from https://www.worldometers.info/coronavirus/country/belgium/

Belgium: new coronavirus cases October 3, 2020 | Statista. (2020). Retrieved 9 October 2020, from https://www.statista.com/statistics/1101080/coronavirus-cases-in-belgium/

How to Find R-Squared in Excel? Use (RSQ) Function. (2020). Retrieved 9 October 2020, from https://www.exceltip.com/statistical-formulas/how-to-find-r-squared-in-excel-use-rsq-function.html

Taylor-Jackson, A. (2020). The 5 Different Trend Lines Explained - The Data School Australia. Retrieved 9 October 2020, from https://www.thedataschool.com.au/alex-taylor-jackson/the-5-different-trend-lines-explained/

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