Introduction
The task requires a detailed investigation to find out the data provided which include the reference number of state and territories, date of onset, notification date which is relevant to the health authority, age, sex and the postcode of residence. The feature and the extensiveness of the data are accumulated in the National Notifiable Diseases Surveillance System which are been influenced with many factors. The Notifications may be from the hospitals and laboratories. Adding, device of the notifications is between the state and territories are noticeable with different mechanisms. Health care provide the number of cases that subject the health authorities for many diseases and may fluctuate among diseases.
The purpose of this task is to make predictions of the future trends which regards to the number of flu cases in Australia for rest of the 2019. A set of flu data with a polynomial value of 3 or more with more suitable parameters and assumptions to develop a model and the implications of my model. All the models which I made will be compared to their accuracy and plausibility.
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Observation and assumptions
The primary observation of the task is to see that influenza season can be very different from one year to another, viruses of influenza changes, and different strains which can circulate in the population. It was expected that the number of people imposed with the flu has been changed. The frames which is useful for real-life applications with realistic outcome. With the observation, the following assumptions are determined.
- People who have been vaccinated then there will less likely to get the diseases like flu in their community. This is valid assumption, because of efficiency of vaccines.
- A number of people who get the flu in 2015, 2016, 2017 and 2018 is more but in 2019 its decreasing.
- As compared to last 3 years in 2019 impact of influenza on people is fewer. In 2018, less than or 11% of the beds were available in FLuCAN hospitals were occupied by the patient with a confirmed influenza.
- Getting a flu shot and the influenza vaccination each year is one of the best to prevent the flu.
Mathematical concepts and the procedures
Online programming DESMOS has been used to determine the unknown parameters because this is an efficient way to visually to see how the parameters will transform an equation. A variety of cubic functions will be used to solve the problem and to make predictions of future trends with regards to a number of flu cases in Australia for the rest of 2019.
The polynomial function can also be written as:
P(x) = anxn+an-1xn-1+…+a1x+a0
Where n is a natural number or zero and the≠0
- Number 0 is called the zero polynomial
- Degree of polynomial is the index n of the leading term
- A monic polynomial is a polynomial in which the leading term has coefficient of 1
- The constant term is the term of index 0
The given polynomial function from a power of 3 and more.
Functions with power 3 y= ax3+bx2+cx+d
Functions with power 4 Y= ax4+bx3+cx2+dx+e
Functions with power 5 Y= ax5+bx4+cx3+dx2+ex+f
Functions with power 6 Y= ax6+bx5+cx4+dx3+ex2+fx+g
Determining the mathematical models:
A set of data has been collected from different years for different genders and ages to make a prediction of flu cases in the rest of 2019 in Australia.
TABLE 1 (RAW DATA)
These are the results that were gathered. The settings are described in “Formulate”. A number of notifications of influenza were recorded from 2008 to 2018 in Australia to get an overall judgment. This will give me data to work with, in order to compare the number of influenzas in different months and years and to differentiate which one worked the most efficiently.
TABLE 2 (Graph of Influenza from 2010-2018)
I have taken a decision to eliminate those few in order to get an even more accurate average of the scenarios which could take place in real-life situations. If you see the averages of influenza in different years average increase in every year but the government isn’t taking any actions towards the influenza flu if it gets going this will definitely caused many problems.
Figure 1.0 Number of people inflicted with flu by age group in 2019
Number of people Age group
4524 00-04
4084 05-09
1965 10-14
2116 15-19
2349 20-24
2476 25-29
2752 30-34
2684 35-39
2284 40-44
2334 45-49
2270 50-54
2358 55-59
2300 60-64
1940 65-69
1717 70-74
1464 75-79
1278 80-84
1839 85+
This figure shows the number of people get inflicted with influenza in different era groups in 2019. In this graph it shows that younger people are more endangering to get influenza as compared to older people. If the young generation will get the vaccination then this flu on the youth will definitely decrease.
Median: 2292
Mode: 2270
Mean: 2172.39
Average: 2374.11
Figure 2.0
This figure shows that most of the people who got inflicted with the flu is in September and about 40000 people were get inflicted with influenza. As in figure 2.0 state the y-intercept of the graph and in the area that the more people in September got the flu. The y-intercept is equal to 11778 which mean that most person get were inflicted in September in 2015. The R2 value is not close to 1 and that’s because of increasing the number of people inflicted with influenza after June until September which the gravity is positive and decreasing the number of people inflicted with influenza from September to November which the gravity is negative.
Figure 3.0
This figure shows the number of people inflicted with flu each month in 2016. Most of the people were inflicted with flu in August which is nearly about 30000 and the y-intercept of the function happens there. The y-intercept is 11723 and it’s in the first quartile which both x and y values are positive. If you compare year 2015 and 2016 then you will see that a smaller number of people got inflicted with influenza in 2016 than 2015. If you see R2 value is closer to 1 in the number of people inflicted with flu in 2016 than the number of people inflicted with in 2015.
This has been predicted that a number of people inflicted in 2016 was less than the number in 2015.
Figure 4.0
This figure shows the number of people who got inflicted in each month in 2017. Most of the people who were inflicted with influenza between august and September about 1 lakh people and the y-intercept of the function happens here. If you see R2 value is not equal to 1, if it is then this graph is not correct. This has been predicted that number of people been affected in 2017 is much more than in 2014, 2015 and 2018
Figure 5.0
In figure 4.0 and 5.0 shows the number of flus cased in each month in 2017 and 2018. As in figure 4.0, there were more people who got inflicted with flu in year 2017 than the recent years. The y-intercept on the graph of 2017 is at a higher point than the y-intercept on the graph of year 2018 and as compared to both year there were more people who has been got inflicted with influenza in 2017. The R2 value on the graph in 2018 is closer to 1 than the R2 value on the graph in 2017 it means that the number of flu cases in each month in 2018 than the graph of the number of flu cases in each month in year 2017.
Table 3: Flu cases in QLD from 2011 to 2018
Average of flu cases in QLD from year 2011 to 2018
TABLE 3
Influenza notifications from 2010-2018 in different states and territories
Table 3 shows that the number of flu cases from 2010 to 2018 from the different territories and states
Prediction of future trends with regards to the number of flu cases in Australia for the rest of 2019
For calculating a number of flu cases from May to December in 2019, we have to sub the no of months into the equation to find the f(x).
May 6649.325
June 12582.716
July 18136.843
August 22047.212
September 23049.329
October 19878.7
November 11270.831
December 9587.411
May -210.749(5)3+ 3603.85(5)2 – 14530.8(5)+ 15550.7
June -210.749(6)3+ 3603.85(6)2 – 14530.8(6)+ 15550.7
July -210.749(7)3+ 3603.85(7)2 – 14530.8(7)+ 15550.7
August -210.749(8)3+ 3603.85(8)2 – 14530.8(8)+ 15550.7
September -210.749(9)3+ 3603.85(9)2 – 14530.8(9)+ 15550.7
October -210.749(10)3+ 3603.85(10)2 – 14530.8(10)+ 15550.7
November -210.749(11)3+ 3603.85(11)2 – 14530.8(11)+ 15550.7
December -210.749(12)3+ 3603.85(12)2 – 14530.8(12)+ 15550.7
The data gathered shows that the flu cases in Australia will increase for the rest of 2019 and for the rest of 2019 more people will inflict with flu.
Evaluation
A major factor behind this task is to see how realistic the models are and if they can be used dependably to interpose the values that are plausible. This allows the validity of the model to be verified. Data from different states and territories make a pattern that the number of flu cases in every state is different. The figures of 2014, 2015, 2016, 2017, 2018 and 2019 undoubtedly show that the fu cases is decreasing from 2014 to 2016 and from 217 to 2018 it increases again. The data also shows that people who got inflicted with flu in 2019 is even higher than the people in 2017 and 2018 from January to April. And for the rest of 2019, its predicted that the number of people with flu will increase.
Conclusion
Using the function to model the polynomial to make a prediction of the future trends with regards of the number of flu cases in Australia for rest of 2019. By using all the given functions, models were obtained by fitting the function in them. The validity of each model was to test the correlation coefficient, remaining analysis and the real-world application. All models had drawbacks. The polynomial models from the given data has the potential to produce a reasonable and better model to make it more realistic values for the variables.
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