{"id":9336,"date":"2023-01-27T10:33:39","date_gmt":"2023-01-27T15:33:39","guid":{"rendered":"https:\/\/blogs.mathworks.com\/student-lounge\/?p=9336"},"modified":"2025-02-21T10:00:58","modified_gmt":"2025-02-21T15:00:58","slug":"youve-got-to-be-modeling-me","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/student-lounge\/2023\/01\/27\/youve-got-to-be-modeling-me\/","title":{"rendered":"You\u2019ve Got to be Modeling Me"},"content":{"rendered":"
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Joining us today is Wesley Hamilton, who is a STEM Outreach Engineer here at MathWorks. Wesley will talk about tackling the 2019 MathWorks Math Modeling Challenge (M3C) problem. <\/span>Wesley, over to you… <\/span><\/div>\n
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Introduction<\/h2>\n
Hello all, I’m Wesley and in this blog post we’ll start tackling the 2019 MathWorks Math Modeling Challenge (M3C) problem<\/a>. The M3C is a free, annual math modeling competition for high school (HS) juniors and seniors in the U.S. and sixth form students in England and Wales, and is a program of the Society of Industrial and Applied Math. More information about the M3C can be found on their website<\/a>, including two free workbooks<\/a> aimed at preparing participants and their coaches to take part in the M3C!<\/div>\n
Here we’ll tackle the 2019 M3C problem by building an initial model for the first part of the challenge. To do this we will make use of best modeling practices, including identifying variables and making assumptions, as well as use MATLAB\u2019s data analysis and curve fitting toolboxes to support our modeling process. Note that this approach isn\u2019t the only way teams might approach this problem (though some of the top submissions did something similar!); our goal is to see what a<\/span> start might look like.<\/div>\n
M3C problems consist of three parts. The first part is designed to be doable by most, if not all, teams. The next two parts typically build on work from the first part, but feature more open-ended questions that let teams showcase their creativity and technical prowess when developing models and solutions to the stated questions. As I mentioned, we\u2019ll focus in on part 1 of the 2019 M3C problem and set ourselves up with a solid start for tackling the rest of the challenge.<\/div>\n
The general outline we’ll follow is<\/div>\n
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  1. read the problem in its entirety,<\/li>\n
  2. formulate a plan to answer the problem,<\/li>\n
  3. carry out our plan.<\/li>\n<\/ol>\n
    Throughout this process we’ll make use of MATLAB, a scientific and engineering programming language developed by MathWorks. If you’re new to MATLAB (or programming), MathWorks has a free OnRamp<\/a> to help you get started. Teams taking part in the M3C can request complimentary MATLAB<\/a> licenses for the competition. Some of these resources (and much more!) can be found on the M3C’s “Learn Technical Computing” website<\/a>.<\/div>\n
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    Table of Contents<\/span><\/div>\n
    Introduction
    \n<\/a>    Initial reading of the problem
    \n<\/a>    Examining the attachments and data
    \n<\/a>    Initial plan for model
    \n<\/a>    Reading in and processing the data
    \n<\/a>    Quick Live Script housekeeping
    \n<\/a>    Building a model by fitting a curve
    \n<\/a>    Comparing to historical data
    \n<\/a>    Summary of progress and next steps<\/a><\/div>\n<\/div>\n
    <\/div>\n

    Initial reading of the problem<\/h2>\n
    Let\u2019s start by reading the part 1 problem statement<\/a> in its entirety (in the actual competition we’d read the entire problem). In addition to setting the stage for why someone might want to know the answer to these questions, the introduction often contains pieces of information that will be helpful to us as we answer the questions.<\/div>\n
    We\u2019ll start by reading the introduction for context of the problem:<\/div>\n
    Substances such as tobacco, alcohol, and narcotics can affect the physical and mental health of users. The consequences of substance abuse, both financial (health care, the criminal justice system, workplace productivity, etc) and non-financial (divorce, domestic abuse, etc), ripple through society and affect more than just the user. The effects of substance abuse on individuals and society have come to the forefront recently as opioid addiction has become prominent [<\/span>1<\/span><\/a>].<\/span><\/div>\n
    We see they provide a reference to an NPR article on Opioid overdoses in the United States. Let\u2019s hold off on looking at the article until we finish reading the problem statement:<\/div>\n
    Efforts, such as taxes and regulations on cigarettes and the Drug Abuse Resistance Education program, have been made at the local, state, and national level to educate, control, and\/or restrict the consumption of such substances. Such efforts need to start with an understanding of how substance abuse spreads and affects some individuals more than others.<\/span><\/div>\n
    Now to part 1, what we are actually being asked to do:<\/div>\n
    Darth Vapor<\/span>\u2014Often containing high doses of nicotine, vaping (inhalation of an aerosol created by vaporizing a liquid) is hooking a new generation that might otherwise have chosen not to use tobacco products. Build a mathematical model that predicts the spread of nicotine use due to vaping over the next 10 years. Analyze how the growth of this new form of nicotine use compares to that of cigarettes.<\/span><\/div>\n
    The last two sentences are key, and worth repeating: “Build a mathematical model<\/span> that predicts the spread of nicotine use due to vaping over the next 10 years. Analyze how the growth<\/span> of this new form of nicotine use compares to that of cigarettes.\u201d<\/div>\n
    So, our task is to model the spread of nicotine use due to vaping and compare our model to the usage of cigarettes. Some questions I already have in mind are: how do we measure the spread or use? Do we keep track of vape usage by the number of cartridges used? By number of users?<\/div>\n
    If you don\u2019t know how vaping works, this would be an opportunity to perform some research to inform some of the questions we\u2019re coming up with. Let\u2019s open a new MATLAB Live Script<\/a> to start taking notes, starting with the tasks of part 1; let\u2019s convert this to \u201ctext\u201d, and then copy over the two key sentences.<\/div>\n
    \"view_1.gif\"<\/div>\n

    Examining the attachments and data<\/h2>\n
    Now let\u2019s look at the provided data<\/a>. Let\u2019s start with the Figure on historical cigarette usage. \u201cAdult* per capita cigarette consumption and major smoking and health events, United States, 1900\u20132012.\u201d<\/div>\n
    \"view_figure.png\"<\/div>\n
    The first thing we should take note of as we look at this graph is the labels on the axes. The x-axis has time in years, and the y-axis is labeled \u201cper capita number of cigarettes smoked per year\u201d. If you\u2019re not sure what per capita means, you should take a moment to do a search for that term so you can fully understand the meaning of the data you have. A quick search turns up that the phrase per capita is often used to replace the words \u201cper person\u201d. So, this data gives us the average number of cigarettes consumed per person each year. This data does not tell us what percentage of the population smokes. However, we can make an assumption that if we did have that data, it might \u201clook\u201d similar to this data in terms of shape. Let\u2019s capture that assumption in our Live Script. If we have time later on, we might search for data to support this assumption.<\/div>\n
    \"view_3.gif\"<\/div>\n
    Speaking of shape, next we might examine the shape of the curve. It starts near zero on the y-axis, hits a peak in the 1960s and 1970s, and then decreases. The shape of this curve reminds me of a Bell curve, or Normal distribution, also called a Gaussian, from probability theory.<\/div>\n
    Now let’s take a look at the provided data, starting with the \u201chigh_school_vaping_data.xlsx\u201d data. The title of the actual spreadsheet is \u201cPercentage of High School Students who used e-cigarettes in the past 30 days, by gender and race\/ethnicity; National Youth Tobacco Survey, 2011-2015\u201d.<\/div>\n
    \"hs_vaping_data_spreadsheet.png\"<\/div>\n
    This data looks to be for all<\/span> HS students (9th through 12th grade), and splits it up based on gender and race\/ethnicity. Already it looks like we\u2019ll need to do a little pre-processing if we want to read in the data, because it includes the percentage along with a confidence interval in parentheses in each cell (think of a confidence interval as the error bounds coming from the survey sampling); for MATLAB to happily read it in, there should be a single number in each cell. We also don\u2019t know (without extra research) what percentage of HS students are White or Hispanic\/Latino, so we might have to put in extra work if we want to mix and match the data objects that aren\u2019t in the \u201cOverall\u201d row.<\/div>\n
    Finally, let\u2019s look at the \u201cNIH-DrugTrends-DataSheet.xlsx\u201d.<\/div>\n
    \"hs_drug_data_spreadsheet.png\"<\/div>\n
    This contains a lot more data on various drugs, but especially relevant for us we see the row corresponding to \u201cany vaping in the past month\u201d. This data is for the years 2015 to 2018, and is split amongst 8th grade, 10th grade, and 12th grade. Also, because of how the data is formatted, we\u2019ll have to perform a little pre-processing before we can read it into MATLAB (like the other spreadsheet). Since the other data is for the years 2011 – 2015, we might want to merge the two datasets so we have data for HS vape usage from 2011 – 2018, which gives our model more to work with. We can justify this by making an assumption that “the National Youth Tobacco Survey and NIH Drug Trends data are comparable”. We’ll have to decide which dataset we use for the 2015 data, but we can do that after we’ve read the data in and are starting to build the model.<\/div>\n
    \"view_3.gif\"<\/div>\n

    Initial plan for model<\/h2>\n
    Now that we\u2019ve taken a look at the provided data, let\u2019s formulate an initial plan of attack to get started with a solution. For assumptions so far we have:<\/div>\n