Smoking Dynamics of Students in High School
Let’s develop a model to describe the smoking dynamics of students in a high school. Let S(t) denote the number of smokers at time t, P(t) the number of potential
smokers at time t, and Q(t) the number of smokers who quit permanently. Further, we define the following model parameters: • c : The average number of contacts between
individuals at school • q : Probability of becoming a smoker given that a potential smoker P has contact with a smoker S. • 1/µ: The average time in the high school
system • 1/γ: The average time spent as a smoker • N(t): Population size at time t • β = qc A model to describe the dynamics of smoking among students is given by: dP
dt = µN − βP S/N − µP dS dt = βP S/N − (µ + γ)S dQ dt = γS − µQ Study the dynamics of the model by completing an equilibria/stability analysis. Explore conditions
under which there will be no smoking in the school, as well as conditions under which smoking persists. Highlight your results by simulating the model. You can use the
results of the equilibria/stability analysis to determine appropriate values for the model parameters. When graphing solutions, illustrate how P, S, and Q vary over
time. Model extension (1): Consider the case in which individuals who have quit smoking (Q) pick up the habit again (this is actually very common). Write down a new
model that describes this phenomenon. Explain this new modification in detail. In this case, you do not need to analyze the new dynamics. However, by doing so, you may
be awarded extra bonus marks (see Grading information below)! 1 Model extension (2): Alter the model by making one further modification to make it more realistic
(choose any modification you want!). Explain this new modification in detail. Important: You must illustrate your results with numerical simulations, and attach your
Matlab code in an Appendix. A brief summary of how you should prepare your report: All projects should include an introduction, a methodology/modeling section, a
results section, and a conclusions/discussion section. If you use any references in your project, you should also include a bibliography. • A good introduction should
give a detailed description of the project objectives, the signifi- cance of the research, the modeling approach, as well as an overview of the main results. • The
methodology/modeling section should include a detailed description of the development of the model. This includes a description of all model assumptions, as well as a
description of the model parameters and variables. • In the results section, you should include all model analysis, as well as figures that illustrate examples of the
important findings. • Finally, in the discussion/conclusion section, you should summarize the most important findings of your project. Include a summary of the results
you found. • Further, a good discussion section should include a discussion of the models limitations, as well as some potential directions you could explore to make
the model more realistic (this should include the modifications you introduced). • All projects need to be written using Word or LaTex. All projects should range
between 10 and 25 pages (if you need to go over the limit a little, that’s OK). • Include code in an appendix. • You will be graded on grammar, spelling, writing
style, and presentation. A good paper should be written in a clear and concise fashion. Please see the grading rubric I included on the Moodle webpage to get a better
understanding of how your projects will be graded. This rubric will highlight more clearly what needs to be in your report. Plagiarism: You are expected to submit your
own work for this project. If you make use of an idea from another source you are expected to provide a citation. If you copy the words from another source you are
expected to put them in quotes and provide a citation. If you make use of a figure or diagram from another source you are expected to provide a citation. To do
otherwise is plagiarism. Any submission found to plagiarize another work will receive a zero. 2 Grading: Your project will be given a letter grade, similar to that
assigned on the course syllabus. However, very exceptional papers will be awarded an A++ (105). That is, you have the potential of being awarded 5 extra points. The
grade of an A++ is reserved for truly exceptional papers. To receive an A++ a team must go beyond the requirements listed above (i.e., they must more fully explore the
problem). For example, the team may extend the model beyond that which is expected and analyze how this extension changes the results of the original model (i.e., like
those you included when you were asked to modify the model). Alternatively, the team may go well beyond the computational requirements for this class. 3 Cover Page –
Staple this to the front of your project Title: Author 1: Author 2: This report is our work. Any help, insight, or aid that we have received is explicitly
acknowledged. To do otherwise is plagiarism, and we understand that we will receive a zero on this report if it is found that we did not adequately acknowledge the
contribution of anybody else. Signature 1: Signature 2: 4
