Math 19Mathematical ModelingProject DescriptionT. JudsonFall 2002The Project DescriptionYour assignment is to either critique one of the articles listed below or for-mulate and analyze a mathematical model for the situation described in oneof the articles. If you decide to formulate a model for the situation describedby the article, you may wish to look at how the article, “The Case of theMissing Meat Eaters,” was analyzed in Chapter 12 or how the article, “LeftSnails and Right Minds,” was analyzed in Chapter 5. If you decide to cri-tique an article such as “Malaria: Focus on Mosquito Genes,” you must doso from a mathematical standpoint and not simply from the viewpoint ofwhether the biology will or will not work.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. 219–224.5. “Diffisional Mobility of Golgi Proteins in Membranes of Living Cells,”pp. 230–237.16. “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.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.• Competing species model:dxdt= αx − βx2− γxy,dydt= δy − λy2− σxy.2• 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.The Final ReportThe project is due on Friday, January 10, 2003. The report must b e typed in12 point type, double spaced with 1.25 inch margins, and the page numberson each page in the upper righthand corner. Typing mathematical symbolsand formulas is a sophisticated skill. Please write mathematical expressionsby hand unless you know how to write expressions correctly with a wordprocessor. Take care to write your report in proper English. A significantpart of your grade will be based on exposition.• A title page containing:– Title of the report– Course name and numb er– Author’s name– Date completed• The report. The body of your report may not exceed 10 pages.• References.• Appendix. The appendix may contain information such as graphs,calculations,
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