Infectious rate of different epidemic diseases
This essay should be about logistic function and its application in predicting the infectious rate of different epidemic diseases.
It should involve lots of calculation steps and accurate math terminologies.
It would be better if the essay makes use of calculus (high school level differentiation and integration) and statistics.
The academic standard is IB mathematics HL (higher level).
Infectious rate of different epidemic diseases
What is your current aim and rationale with the project?
Recently, the outburst of Ebola in the west Africa has claimed more than 4,800 lives and this number is sure to rise. Other epidemic diseases around the world or in the history has affected the society or even the basis of civilization, such as the notorious Black Death, influenza, bird flu, SARS and HIV.
The essay aims to explore the speed of the infection of different diseases and see how factors such as technological advancement, mode of transmission, nature of the virus and locations affect the rate of infection. After a general formula of the infection rate is generated, these factors would be represented as mathematical constant in the equation.
Ideally, after comparing different epidemics, the essay would also propose a graph that plots he fatality ratio against the chronological order of history to see how development is hygiene and medical sciences has helped reducing the fatality and infection of different epidemics (though I am afraid the number of different epidemics that can be incorporated into this final graph would be limited because of time constraint, which may lead to an insufficient conclusion).
How will you use mathematics to achieve this? What mathematics will be used? Include specific topics you believe you believe will have to use in your exploration.
The epidemic model of infectious rate involves the appliance of various functions (exponential, logarithm and etc.) and potentially simple knowledge in statistics.
The actual interpretations of the statistics and the model built would largely rely on the knowledge of differentiation and integration, especially methodology introduced in 16.9 (differential equations)
What opportunities will there be for you to critically reflect on your work? Have other people attempted what you are trying to do? Make a note of these people here.
Limitation in statistics: It may be difficult to acquire accurate data of patients and death because identifying the disease needs time and there might be misjudgment in the early stage of diagnosing that some deaths would be attributed to other disease or vice versa.
Different diseases might have different ways of transmission, thus having different pattern of infection over time. If the essay fails to give a conclusion about the universal pattern of epidemics, reflection can be done
The statistics in terms of infection of the diseases should be available online from different resources. The modeling of infection rate has already been widely discussed and well established. Terminologies such as the basic reproductive rate (Ro) and fatality ratio would be useful in elucidating the concepts
https://wenku.baidu.com/view/3b3a1f0a84868762caaed5c0.html
https://www.cdc.gov/flu/weekly/index.htm
How will you be able to demonstrate a significant amount of personal engagement with this topic? Is there an opportunity for you to use the mathematics you discover in a new or creative way? Can you extend your work to take into account other areas of mathematics?
Since the topic involves a lot of biology, I will have to read more about the background information of diseases as well as the contemporary medical condition. The actual process of using differentiation and integration for mathematic model is also new to me, so I will have to learn this portion of math by myself.
The data collected can be presented in a very creative way and thus knowledge in statistics can be applied to optimize the graphical representation.
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