• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17
  18. 18
    18
  19. 19
    19
  20. 20
    20
  21. 21
    21
  22. 22
    22
  23. 23
    23
  24. 24
    24
  25. 25
    25

Modelling the H1N1 Epidemic in Canada

Extracts from this document...

Introduction

IB Maths SL Internal Assessment | Tanya Waqanika

CITY AND ISLINGTON SIXTH FORM COLLEGE

IB Maths SL Internal Assessment

Modelling the re-emerging H1N1 virus in Canada

Tanya Waqanika

Table of Contents

Rationale

Background

Epidemiology

The SIR Model

The SIR Model’s Differential Equations

The S – Susceptible equation

An Alternative Method for Plotting the SIR model on a Graph

Applying the SIR Model to the Re-Emerging H1N1 virus in Canada

The Basic Reproductive Numberand β

Applying the Calculated Values from the data on the SIR Model

Vaccination and Herd Immunity with the Basic Reproduction Number

Conclusion and Reflection

Appendices

Appendix 1 – Excel data used to produce Graph 2

Appendix 2 – Model, Graph and Calculations for Graph 3

Bibliography

Rationale

As I would like to study Medicine in the future, I decided to investigate the mathematics of epidemiology. Epidemiology is also interesting to me because the constant and fast evolution of dangerous pathogens and diseases often threatens the human population. In the last few decades alone, epidemics such as AIDs, Measles, Avian Influenza (H5N1) and Swine Influenza (H1N1 (pdm09)) have caught the attention of the world. 2009 was a particularly significant year, as a certain strain of Swine Influenza was declared by the World Health Organisation to be potentially pandemic due to a series of epidemics all over the world. Even though the world never succumbed to a Swine Influenza pandemic, in December, a published article stated H1N1 was re-emerging in Canada.[1] This caused a stir in the public and encouraged individuals to get themselves vaccinated against H1N1 to prevent another epidemic breaking out. Having lived in Canada for a year, this situation was incredibly interesting and relevant to me as I have a lot of friends and family living in Canada as well.

...read more.

Middle

dt). With this definition, I can then employ Euler’s method[5] to devise a simpler way of producing a line that is approximate to the line produced by the rate of change in the S compartment as the epidemic progresses. Remembering that S in the SIR model is a function of time, I can use this formula to produce a similar equation for S.

image21.png
Formula  taken from [http://en.wikipedia.org/wiki/Euler_method]

If we then assume that dS/dt can be written as:

image07.png

Where:

dS/dt --βSI
(n + 1)
 – Any time in the future
n – The present time

I can then rearrange this in terms S, which would give an approximate formula for the integration of dS/dt:

image09.png

The same method applied to dI/dt devises the suitable formula for its approximate integration as well:

image10.png

To keep the model simple, we can rely on the previous assumptions made about the SIR model. Since S + I + R = N, we can rearrange this to make R = N – S – I. When this is written in a similar form to the formulas above, we get:

image11.png

Applying the SIR Model to the Re-Emerging H1N1 virus in Canada

The population of Canada is approximately 35,295,770[6]. Within the population 8,292,255[7] is the estimated number of Canadians vaccinated against H1N1 since 2012. The Canadian government has a website called FluWatch, which collects data from all over Canada concerning the number of cases that crop up from each type of influenza strain. The very first case of H1N1 was detected on August 25th 2013 and FluWatch carefully monitors the number of H1N1 cases that are detected and publishes these numbers every week. I have been collecting these cases and have presented them in the following table:

Week

Number of Cases

35

4

36

1

37

0

38

1

39

1

40

2

41

2

42

1

43

1

44

14

45

19

46

38

47

38

48

73

49

145

50

281

51

503

52

808

53

1378

...read more.

Conclusion

Understand Seasonal Flu, Human Swine Flu and Hand-Foot-Mouth Diseases. 2014. [e-book] Hong Kong: Centre for Health Protection. p. 19. Available through: Centre for Health Protection http://www.chp.gov.hk/files/pdf/understand_seasonal_flu,_human_swine_flu_and_hand-foot-mouth_diseases_eng.pdf [Accessed: 13 Feb 2014].

Using Calculus to Model Epidemics. 2014. [e-book] Available through: homepage.math.uiowa.edu http://homepage.math.uiowa.edu/~stroyan/CTLC3rdEd/3rdCTLCText/Chapters/Ch2.pdf [Accessed: 13 Feb 2014].

Wikipedia. 2014. Epidemic model. [online] Available at: http://en.wikipedia.org/wiki/Epidemic_model [Accessed: 13 Feb 2014].

Wikipedia. 2014. Euler method. [online] Available at: http://en.wikipedia.org/wiki/Euler_method [Accessed: 13 Feb 2014].

Wikipedia. 2014. Basic reproduction number. [online] Available at: http://en.wikipedia.org/wiki/Basic_reproduction_number [Accessed: 13 Feb 2014].

Wikipedia. 2014. List of countries by life expectancy. [online] Available at: http://en.wikipedia.org/wiki/List_of_countries_by_life_expectancy#List_by_the_World_Health_Organization_.282013.29 [Accessed: 13 Feb 2014].

Wikipedia. 2014. Herd immunity. [online] Available at: http://en.wikipedia.org/wiki/Herd_immunity [Accessed: 13 Feb 2014].

Wikipedia. 2014. Mathematical modelling of infectious disease. [online] Available at: http://en.wikipedia.org/wiki/Mathematical_modelling_of_infectious_disease [Accessed: 13 Feb 2014].

 | Page


[1] http://www.ctvnews.ca/health/h2n1-virus-what-you-need-to-know-1.1609554

[2] http://www.oxforddictionaries.com/definition/english/epidemiology

[3] http://homepage.math.uiowa.edu/~stroyan/CTLC3rdEd/3rdCTLCText/Chapters/Ch2.pdf

[4] http://en.wikipedia.org/wiki/Epidemic_model

[5] http://en.wikipedia.org/wiki/Euler_method

[6] http://www.statcan.gc.ca/start-debut-eng.html

[7] http://statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/health202a-eng.htm

[8] http://en.wikipedia.org/wiki/Basic_reproduction_number

[9] http://en.wikipedia.org/wiki/Mathematical_modelling_of_infectious_disease

[10] http://en.wikipedia.org/wiki/List_of_countries_by_life_expectancy#List_by_the_World_Health_Organization_.282013.29

[11]http://en.wikipedia.org/wiki/Basic_reproduction_number; http://www.chp.gov.hk/files/pdf/understand_seasonal_flu,_human_swine_flu_and_hand-foot-mouth_diseases_eng.pdf

[12] http://motivate.maths.org/content/DiseaseDynamics/Activities/Modelling

[13] http://en.wikipedia.org/wiki/Herd_immunity

[14] http://en.wikipedia.org/wiki/Basic_reproduction_number

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Math Studies I.A

    Convenience sampling is not used as it is not very scientific or systematic and human emotion interference causing bias. The assumption made is that there is a linear correlation. However, the value of r turns out to be not very strong.

  2. Math IA -Modelling Population Growth in China.

    Hit the 2nd key, then hit the 1 key. This should make a L1 appear behind the LinReg(ax+b). After you have the L1 behind the LinReg(ax+b), hit the comma button (,). Then hit the 2nd button again and then the 2 button. This will make your screen look like this: LinReg(ax+b)

  1. Maths IA Type 2 Modelling a Functional Building. The independent variable in ...

    Volume of wasted space (m3) Max volume of cuboid (m3) Ratio Volume wasted : Volume cube 75 228230.855 311769.145 0.732 : 1 85 258659.557 353340.443 0.732 : 1 95 28909.494 394905.506 0.732 : 1 110 334740.665 457259.335 0.732 : 1 111 337781.665 461418.335 0.732 : 1 112.5 342346.282 467653.718 0.732

  2. Math Studies - IA

    This can be represented as a scatter plot, which can assist in identifying any correlation between the two variables, and the strength between them. GRAPH SHOWING THE RELATIONSHIP BETWEEN THE OUTCOME IN MAJORS AND THE OUTCOME IN THE RYDER CUP As it appears in the scatter plot with the least

  1. Math IA - Logan's Logo

    The original sine curve starts (meaning it crosses the center line of its curve) at point (0,0), and using this point as a reference, I can determine how many units leftwards my curve has shifted. (I know it has shifted leftwards after comparing my graph to the original sine graph).

  2. Modelling the course of a viral illness and its treatment

    Time before death = 117,3 + 26,6 =143,9. (see figure 2-3) Modelling recovery 3. The medication and immune response can together eliminate 1,2 million viral particles. This means that if a person seeks medical attention have to do it before the replication of viral particles exceed 1,2 million.

  1. Gold Medal heights IB IA- score 15

    Figure 10 shows the interpolated and extrapolated data with the model function This makes sense because the correlation of the data show a slow decrease in slope and therefore the year 1984 is near the maximum point. Furthermore, the year 2016 is a very far extrapolation from the given data points.

  2. MATH Lacsap's Fractions IA

    I will be considering the relationship between the numerator and denominator. The denominators will be categorized into different elements (as shown in Figure 3) and analysed individually. ________________ The tables below show the relationships between the row number (n)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work