Math 442 Final Project - Spring 2015
Due Monday, May 4th
Directions: You will work individually to develop a mathematical model
for a system of your choice. You will then complete a basic analysis of your
model and perform numerical simulations. You are responsible for writing
your own Matlab and LATEX code. You are to split the writing tasks and
critique each others work, bringing everything together into one coherent
report at the end.
The final project will consist of two parts: (1) a report prepared in LATEX
describing your modeling goals, model development, mathematical analysis,
numerical results, and conclusions, and (2) a ten-minute presentation prepared using the beamer document class in LATEX in which you explain your
modeling goals, methods, results, and conclusions.
Part 1: Report
You will prepare and submit a formal report using LATEX. Your target
audience is a group of undergraduate students who have completed courses
in linear algebra and differential equations, but may have forgotten some of
the techniques from these courses. The report must include the following:
1. Introduction
In the introduction, you should give some background information on
the system you will model and state your goals in modeling the system.
Try to answer the following questions:
• What system are you modeling?
• Why is the study of this system important?
• Has anyone already developed a model(s) of this system? If so,
what were the results of their study? In what ways is your model
similar/different to the previously developed model(s)?
• What are the goals of your study?
• What were the major conclusions of your study?
2. Methods
In the methods section, you should describe the development of your
model, and present a mathematical analysis. If developing an epidemic
model, the methods section should include:
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• A compartmental diagram.
• The definition of all variables/parameters, and their biological
significance.
• The system of equations which define your model.
• Your modeling assumptions.
• Calculation of a unique disease-free equilibrium (DFE), if one
exists.
• Calculation of an expression for the basic reproduction number,
R0 , and a biological interpretation of this expression.
• Discussion of the stability of the unique DFE.
• Calculation of a unique endemic equilibrium (EE), if possible.
• Discussion of the stability of the unique EE, if possible.
• Discussion of possible disease control strategies.
If developing some other model, the methods section should include:
• The definition of all variables/parameters, and their biological
significance.
• The system of equations which define your model.
• Your modeling assumptions.
• Calculation of all equilibria and a discussion of their stability, if
possible.
3. Results
In the results section, you should include a table of the parameter
values you will use for numerical simulations (along with the sources
for the parameter values, if possible), the values of R0 , the DFE, and
the EE with these parameter values, the initial conditions you will use,
the results of your numerical simulations (included as LATEX figures)
and a biological interpretation of these results. See if the numerical
simulations confirm your work in the Methods section. Try testing the
efficacy of different disease control strategies and discuss which control
methods seem to be the best.
4. Conclusions
In the conclusions section, summarize the major results of your report
along with any limitations of your work. Describe what you have
learned about the system based on your model and simulations.
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5. References
Include a list of references for your project. These could include articles
describing previously developed models, articles from which parameter
values were taken, articles describing the biological/physical nature of
the system, etc.
6. Appendix
Include your function and script M-files as an appendix to your report.
Matlab code should be well-written, in logical order, and include detailed comments.
Part 2: Presentation
You will prepare a ten-minute presentation summarizing your report using the beamer document class in LATEX. You will present your work to your
instructor and classmates. Be sure to practice your presentation for time
and allow 2-3 minutes at the end for questions! All students will be cut off
after ten minutes.
Note: In addition to turning in a hard copy of your report and Matlab files, Email the LATEX and PDF files for your report and presentation
(along with the corresponding figures), and Matlab files in a zipped folder
to glahodny@math.tamu.edu.
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