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2006年美赛o奖论文集.pdf

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    TheUMAPJournal Publisher COMAP, Inc. Vol. 27, No. 2 校 苑 数 模 . w w w m a t h o r . c o m Executive Publisher Solomon A. Garfunkel ILAP Editor Chris Arney Associate Director, Mathematics Division Program Manager, Cooperative Systems Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 David.Arney1@arl.army.mil On Jargon Editor Yves Nievergelt Department of Mathematics Eastern Washington University Cheney, WA 99004 ynievergelt@ewu.edu Reviews Editor James M. Cargal Mathematics Dept. Troy University— Montgomery Campus 231 Montgomery St. Montgomery, AL 36104 jmcargal@sprintmail.com Chief Operating Officer Laurie W. Arag´on Production Manager George W. Ward Production Editor Timothy McLean Distribution Kevin Darcy John Tomicek Graphic Designer Daiva Kiliulis Editor Paul J. Campbell Campus Box 194 Beloit College 700 College St. Beloit, WI 53511–5595 campbell@beloit.edu Associate Editors Don Adolphson Chris Arney Aaron Archer Ron Barnes Arthur Benjamin Robert Bosch James M. Cargal Murray K. Clayton Lisette De Pillis James P. Fink Solomon A. Garfunkel William B. Gearhart William C. Giauque Richard Haberman Jon Jacobsen Walter Meyer Yves Nievergelt Michael O’Leary Catherine A. Roberts John S. Robertson Philip D. Straffin J.T. Sutcliffe Brigham Young University Army Research Office AT&T Shannon Research Laboratory University of Houston—Downtown Harvey Mudd College Oberlin College Troy University— Montgomery Campus University of Wisconsin—Madison Harvey Mudd College Gettysburg College COMAP, Inc. California State University, Fullerton Brigham Young University Southern Methodist University Harvey Mudd College Adelphi University Eastern Washington University Towson University College of the Holy Cross Georgia Military College Beloit College St. Mark’s School, Dallas
    Subscription Rates for 2006 Calendar Year: Volume 27 Membership Plus Individuals subscribe to The UMAP Journal through COMAP’s Membership Plus. This subscription also includes a CD-ROM of our annual collection UMAP Modules: Tools for Teaching, our organizational newsletter Consortium, on-line membership that allows members to download and reproduce COMAP materials, and a 10% discount on all COMAP purchases. (Domestic) (Outside U.S.) #2620 #2621 $104 $117 Institutional Plus Membership Institutions can subscribe to the Journal through either Institutional Plus Membership, Regular Institutional Membership, or a Library Subscription. Institutional Plus Members receive two print copies of each of the quarterly issues of The UMAP Journal, our annual collection UMAP Modules: Tools for Teaching, our organizational newsletter Consortium, on-line membership that allows members to download and reproduce COMAP materials, and a 10% discount on all COMAP purchases. (Domestic) (Outside U.S.) #2670 #2671 $479 $503 Institutional Membership Regular Institutional members receive print copies of The UMAP Journal, our annual collection UMAP Modules: Tools for Teaching, our organizational newsletter Consortium, and a 10% discount on all COMAP purchases. (Domestic) (Outside U.S.) #2640 #2641 $208 $231 Web Membership Web membership does not provide print materials. Web members can download and reproduce COMAP materials, and receive a 10% discount on all COMAP purchases. (Domestic) (Outside U.S.) #2610 #2610 $41 $41 To order, send a check or money order to COMAP, or call toll-free 1-800-77-COMAP (1-800-772-6627). The UMAP Journal is published quarterly by the Consortium for Mathematics and Its Applications (COMAP), Inc., Suite 3B, 175 Middlesex Tpke., Bedford, MA, 01730, in cooperation with the American Mathematical Association of Two-Year Colleges (AMATYC), the Mathematical Association of America (MAA), the National Council of Teachers of Mathematics (NCTM), the American Statistical Association (ASA), the Society for Industrial and Applied Mathematics (SIAM), and The Institute for Operations Research and the Management Sciences (INFORMS). The Journal acquaints readers with a wide variety of professional applications of the mathematical sciences and provides a forum for the discussion of new directions in mathematical education (ISSN 0197-3622). Periodical rate postage paid at Boston, MA and at additional mailing offices. Send address changes to: info@comap.com COMAP, Inc., Suite 3B, 175 Middlesex Tpke., Bedford, MA, 01730 © Copyright 2006 by COMAP, Inc. All rights reserved.
    Vol. 27, No. 2 2006 Table of Contents Editorial HIV: The Math Paul J. Campbell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Special Section on the ICM Results of the 2006 Interdisciplinary Contest in Modeling Chris Arney . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 The United Nations and the Quest for the Holy Grail (of AIDS) Andrew Mehta, Quianwei Li, and Aaron Wise . . . . . . . . . . . . . . . . . . . 113 Managing the HIV/AIDS Pandemic: 2006–2055 Tyler Huffman, Barry Wright III, and Charles Staats III . . . . . . . .129 AIDS: Modeling a Global Crisis (and Australia) Chris Cecka, Michael Martin, and Tristan Sharp . . . . . . . . . . . . . . 145 The Spreading HIV/AIDS Problem Adam Seybert, David Ryan, and Nicholas Ross . . . . . . . . . . . . . . 163 Judge's Commentary: The Outstanding HIV/AIDS Papers Kari Murad and Joseph Myers . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Author’s Commentary: The Outstanding HIV/AIDS Papers Heidi Williams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
    Editorial 93 Editorial HIV: The Math Paul J. Campbell Mathematics and Computer Science Beloit College Beloit, WI 53511 campbell@beloit.edu Roughly 1% of the world’s adult population is infected with HIV, which currently results in 2.8 million deaths per year (3% of all deaths and almost three times as many as malaria). What can mathematics offer in the struggle against this disease? Mathemat- ics itself offers no protection and no cures. However, like claims early on that “everyone” can get AIDS, and revelations of false assurances of safety of the blood supply in the U.S. and France, mathematics can definitely help add to the scare effect. Many years ago, I rejected for publication in this Journal a paper by a student team that projected that most American adults would be infected by HIV—or dead from it—by now. Both the modeling and the conclusions were unsound. The dynamic of HIV, however, has since taught us again an old les- son, that fear is weaker than desire. (This Journal did publish a UMAP Module on HIV recently [Isihara 2005], dealing mainly with immunological aspects.) What mathematics can do is project immediate past and current trends, to reveal what the future could be without basic change. In the case of HIV, the results are encouraging for some countries and discouraging for others. The teams in this year’s Interdisciplinary Contest in Modeling were asked to focus their modeling on “critical” countries, with the teams determining for them- selves the meaning of “critical” and selecting the countries. The Outstanding papers published here unsurprisingly focus on many of the same countries (ones with large HIV-positive populations or with a large proportion of their population HIV-positive) and project, in human and in economic terms, the results of different strategies of intervention. Mathematics can certainly help quantify the varied consequences of differ- ing policies, such as for preventing HIV. But many people mistrust the predic- tions of mathematics because they mistrust mathematics. And they mistrust The UMAP Journal 27 (1) (2006) 93–94. cCopyright 2006 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.
    94 The UMAP Journal 27.1 (2006) mathematics because they never understood it nor learned to appreciate its relevance. The thousands of interested students who take part in the ICM and MCM are one prong of COMAP’s efforts to promote applications in mathematics in- struction. However, it is those millions of students mistrustful of mathematics whom COMAP tries hardest to reach, with its high school mathematics text- books [COMAP 2000; 2002; 2007; Crisler and Froelich 2006], its college-level textbook [Garfunkel et al. 2006], and other initiatives. References COMAP. 2000. Mathematics: Modeling Our World. 4 vols. Lexington, MA: COMAP. . 2002. Mathematical Models with Applications. New York: W.H. Free- man. . 2007. Modeling with Mathematics: A Bridge to Algebra II. New York: W.H. Freeman. Crisler, Nancy, and Gary Froelich. 2006. Discrete Mathematics through Applica- tions. 3rd ed. New York: W.H. Freeman. Garfunkel, Solomon A., et al. 2006. For All Practical Purposes. 7th ed. New York: W.H. Freeman. Isihara, Paul A., et al. 2005. Immunological and epidemiological HIV/AIDS modeling. UMAP Modules in Undergraduate Mathematics and Its Appli- cations: Module 791. The UMAP Journal 26 (1): 49-–90. About the Editor Paul Campbell graduated summa cum laude from the University of Dayton and received an M.S. in algebra and a Ph.D. in mathematical logic from Cornell University. He has been at Beloit College since 1977, where he served as Director of Academic Computing from 1987 to 1990. He is Reviews Editor for Mathematics Magazine and has been editor of The UMAP Journal since 1984. He is a co-author of the COMAP-sponsored book of applications-oriented collegiate mathematics For All Practical Purposes (7th ed. W.H. Freeman 2006), already used by more than half a million students.
    Results of the 2006 ICM 95 Modeling Forum Results of the 2006 Interdisciplinary Contest in Modeling Chris Arney, ICM Co-Director Division Chief, Mathematical Sciences Division Program Manager, Cooperative Systems Army Research Office PO Box 12211 Research Triangle Park, NC 27709–2211 David.Arney1@arl.army.mil Introduction A total of 224 teams of undergraduates and high school students, from 122 departments in 80 institutions in 6 countries, spent a weekend in Febru- ary working on an applied mathematics problem in the 8th Interdisciplinary Contest in Modeling (ICM). This year’s contest began on Thursday, Feb. 2, and ended on Monday, Feb. 6. During that time, the teams of up to three undergraduates or high school stu- dents researched, modeled, analyzed, solved, wrote, and submitted their solu- tions to an open-ended complex interdisciplinary modeling problem involving public-health policy decisions concerning the HIV/AIDS epidemic. After the weekend of challenging and productive work, the solution papers were sent to COMAP for judging. Four of the top papers, which were judged to be Out- standing by the panel of judges, appear in this issue of The UMAP Journal. Results and winning papers from the first seven contests were published in special issues in 1999 through 2005. COMAP’s Interdisciplinary Contest in Modeling along with its sibling con- test, the Mathematical Contest in Modeling, are unique among mathematics competitions in that they are the only international contests in which students work in teams to find a solution. Centering its educational philosophy on The UMAP Journal 27 (2) (2006) 95–112. cCopyright 2005 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.
    96 The UMAP Journal 27.2 (2006) mathematical modeling, COMAP supports the use of mathematical tools to ex- plore real-world problems. The contests serve society by developing students as problem solvers in order to become better-informed—and better-prepared— citizens, consumers, workers, and leaders. This year’s public health problem was particularly challenging in its de- mand for teams to utilize many aspects of science and mathematics in their modeling and analysis. The problem required teams to understand the science of the HIV virus and understand and model the financial and policy issues associated with controlling the pandemic, in order to advise the United Na- tions on how to manage the resources available for addressing HIV/AIDS. The teams’ job was to model several scenarios of interest and use their models to rec- ommend the allocation of financial resources. In addition, to accomplish their tasks, teams had to consider trends in HIV/AIDS morbidity and mortality, to- gether with historical demographic and health data on fertility, population, age distribution, life expectancy, and disease burden. The problem required analy- sis of issues of many kinds—economic, demographic, political, environmental, social, psychological, plus future technology, along with several challenging requirements needing scientific and mathematical analysis. The problem also included the ever-present requirements of the ICM to use thorough data anal- ysis, creativity, approximation, precision, and effective communication. The author of the problem was Heidi Williams, Ph.D. student in Economics at Harvard University, who served on the panel of final judges. The problem originated from her work with the Center for Global Development (a nonprofit think tank in Washington, DC) to contribute to public policy efforts aimed at speeding the development of (and increasing access to) vaccines for diseases that are concentrated in low-income countries. Commentary on the HIV/AIDS problem from Ms. Williams appears in this issue of The UMAP Journal. All members of the competing teams are to be congratulated for their ex- cellent work and dedication to scientific modeling and problem solving. This year’s judges remarked that the quality of the modeling, analysis, and presen- tation was extremely high and the interdisciplinary modeling very robust. The award levels for this year’s contest reflect the increase in quality. The 2006 ICM was managed by COMAP via its information system con- nected to the World Wide Web, where teams registered, obtained contest ma- terials, downloaded the problem, and also downloaded considerable amounts of provided data through COMAP’S ICM Website. Next year, we will continue with the public health theme for the contest problem. Teams preparing for the 2007 contest should consider reviewing interdisciplinary topics in the area of public health modeling and analysis. Teams should also be aware of the presentation style required for this kind of writing. This contest mirrors reality. A paper will have an impact only if it is read, and most readers make the decision whether or not to read a paper based on the summary and the first few paragraphs of the paper. Although triage judges do spend some time with each paper, they cannot read every paper completely. Therefore, we cannot overemphasize the importance of the
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