Math 19Mathematical ModelingProject DescriptionT. JudsonFall 2006Project DescriptionYour assignment is to either critique one of the articles listed below or formu-late and analyze a mathematical model for the situation described in one ofthe articles. If you decide to formulate a model for the situation described bythe article, you may wish to look at how the article, “The Case of the MissingMeat Eaters,” was analyzed in Chapter 12 or how the article, “Left Snailsand Right Minds,” was analyzed in Chapter 5. If you decide to critique anarticle such as “Malaria: Focus on Mosquito Genes,” you must do so from amathematical standpoint and not simply from the viewpoint of whether thebiology will or will not work.Approved Articles1. “HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell LifeSpan, and Viral Generation Time,” pp. 15–22.2. “Wolves Moose, and Tree Rings on Isle Royale,” pp. 96–102.3. “Malaria: Focus on Mosquito Genes,” pp. 198–2024. “Counting Polymers Moving Through a Single Ion Channel,” pp. 219–224.15. “Diffisional Mobility of Golgi Proteins in Membranes of Living Cells,”pp. 230–237.6. “Direct and Continuous Assessment by Cells by Their Position in aMorphogen Gradient; Activin Signalling and Response to MorphogenGradient,” pp. 296–300.7. “Disparate Rates of Molecular Evolution in Cospeciating Hosts andParasites,” pp. 401–410.8. “Thresholds in Development,” pp. 421–428.You may substitute a different article for one of the above articles with myapproval. If you have specific topic that interests you such as epidemiology,I can suggest other articles.Some Models to ConsiderYou will want to consider one or more of the mathematical models that wehave studied or will study in this course.• Exponential growth model:dPdt= αP.• Logistic growth model:dPdt= αP − βP2.• Epidemic model:dxdt= −λxy + αx,dydt= λxy + βy.• Predator-prey model:dxdt= αx − βx2− γxy,dydt= −σy + λxy.2• Competing species model:dxdt= αx − βx2− γxy,dydt= δy − λy2− σxy.• Advection model:∂u∂t= −c∂u∂x+ f (u).• Diffusion model:∂u∂t= µ∂2u∂x2+ f (u).General RulesYou may consult me or other students for help, but your work and yourreport must be your own.Preliminary ProposalA one-page preliminary proposal of your project is due on Monday, December4, 2006. Your proposal must be typed in 12 point type and double spacedwith 1.25 inch margins.The Final ReportThe project is due on Friday, January 12, 2006. The report must be typed in12 point type, double spaced with 1.25 inch margins, and the page numberson each page must appear in the upper righthand corner. Typing mathemat-ical symbols and formulas is a sophisticated skill. Please write mathematicalexpressions by hand unless you know how to write expressions correctly witha word processor. Take care to write your report in proper English. Asignificant part of your grade will be based on exposition.• A title page containing:– Title of the report3– Course name and number– Author’s name– Date completed• The report. The body of your report may not exceed 10 pages.• References. You may select any style to list your references, but youmust be consistent.• Appendix. The appendix may contain information such as graphs,calculations,
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