2006_年美国大学生数学建模竞赛_mcm_icm_试题
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2006_年美国大学生数学建模竞赛_mcm_icm_试题 [2008/01/12 19:36] amao 创建 |
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| You are a team of analysts advising the United Nations (UN) on how to manage the available resources for addressing HIV/AIDS. Your job is to model several scenarios of interest and to use your models to recommend the allocation of financial resources. The narrative below provides some background information, | You are a team of analysts advising the United Nations (UN) on how to manage the available resources for addressing HIV/AIDS. Your job is to model several scenarios of interest and to use your models to recommend the allocation of financial resources. The narrative below provides some background information, | ||
| - | Task #1: For each of the continents (Africa, Asia, Europe, North America, Australia, and South America), choose the country you believe to be most critical in terms of HIV/AIDS. Build a model to approximate the expected rate of change in the number of HIV/AIDS infections for these countries from 2006 to 2050, in the absence of any additional interventions. Fully explain your model and the assumptions that underlie your model. In addition, explain how you selected the countries to model. | + | **Task #1**: For each of the continents (Africa, Asia, Europe, North America, Australia, and South America), choose the country you believe to be most critical in terms of HIV/AIDS. Build a model to approximate the expected rate of change in the number of HIV/AIDS infections for these countries from 2006 to 2050, in the absence of any additional interventions. Fully explain your model and the assumptions that underlie your model. In addition, explain how you selected the countries to model. |
| There are a number of interventions that HIV/AIDS funding could be directed towards -- including prevention interventions (voluntary counseling and testing, condom social marketing, school-based AIDS education, medicines to prevent mother-to-child transmission, | There are a number of interventions that HIV/AIDS funding could be directed towards -- including prevention interventions (voluntary counseling and testing, condom social marketing, school-based AIDS education, medicines to prevent mother-to-child transmission, | ||
| - | Task #2: First, estimate the level of financial resources from foreign aid donors that you realistically expect to be available to address HIV/AIDS, by year, from 2006 to 2050, for the countries you selected in Task #1. Then use the model you developed in Task #1 and these estimates of financial resources to estimate the expected rate of change in the number of HIV/AIDS infections for your selected countries from 2006 to 2050 under realistic assumptions for the following three scenarios: (1) Antiretroviral (ARV) drug therapy (2) A preventative HIV/AIDS vaccine (3) Both ARV provision and a preventative HIV/AIDS vaccine Assume in these scenarios that there is no risk of emergence of drug-resistant strains of HIV (you will examine this issue in Task #3). | + | **Task #2**: First, estimate the level of financial resources from foreign aid donors that you realistically expect to be available to address HIV/AIDS, by year, from 2006 to 2050, for the countries you selected in Task #1. Then use the model you developed in Task #1 and these estimates of financial resources to estimate the expected rate of change in the number of HIV/AIDS infections for your selected countries from 2006 to 2050 under realistic assumptions for the following three scenarios: (1) Antiretroviral (ARV) drug therapy (2) A preventative HIV/AIDS vaccine (3) Both ARV provision and a preventative HIV/AIDS vaccine Assume in these scenarios that there is no risk of emergence of drug-resistant strains of HIV (you will examine this issue in Task #3). |
| Be sure to carefully describe the assumptions that underlie your model. | Be sure to carefully describe the assumptions that underlie your model. | ||
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| - The year in which an HIV/AIDS preventative vaccine might be available | - The year in which an HIV/AIDS preventative vaccine might be available | ||
| - How quickly vaccination rates might reach the following steady-state levels of vaccination: | - How quickly vaccination rates might reach the following steady-state levels of vaccination: | ||
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| - The efficacy and duration of protection of the vaccine | - The efficacy and duration of protection of the vaccine | ||
| - Whether there would be epidemiological externalities from vaccination | - Whether there would be epidemiological externalities from vaccination | ||
| - Assume the vaccine is a three-dose vaccine, and can be added to the standard package of vaccines delivered under the WHO’s Expanded Programme on Immunization (EPI) at an incremental cost of addition of $0.75 | - Assume the vaccine is a three-dose vaccine, and can be added to the standard package of vaccines delivered under the WHO’s Expanded Programme on Immunization (EPI) at an incremental cost of addition of $0.75 | ||
| - | Task #3: Re-formulate the three models developed in Task #2, taking into consideration the following assumptions about the development of ARV-resistant disease strains. | + | **Task #3**: Re-formulate the three models developed in Task #2, taking into consideration the following assumptions about the development of ARV-resistant disease strains. |
| Current estimates suggest that patients falling below 90-95 percent adherence to ARV treatment are at a “substantial risk” of producing drug resistant strains. Use as an assumption for your analysis that a person receiving ARV treatment with adherence below 90 percent has a 5 percent chance of producing a strain of HIV/AIDS which is resistant to standard first-line drug treatments. | Current estimates suggest that patients falling below 90-95 percent adherence to ARV treatment are at a “substantial risk” of producing drug resistant strains. Use as an assumption for your analysis that a person receiving ARV treatment with adherence below 90 percent has a 5 percent chance of producing a strain of HIV/AIDS which is resistant to standard first-line drug treatments. | ||
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| Second- and third-line ARV drug therapies are available, but assume for your analysis that these drugs are prohibitively expensive to implement in countries outside of Europe, Japan, and the United States | Second- and third-line ARV drug therapies are available, but assume for your analysis that these drugs are prohibitively expensive to implement in countries outside of Europe, Japan, and the United States | ||
| - | Task #4: Write a white paper to the United Nations providing your team’s recommendations on the following: | + | **Task #4**: Write a white paper to the United Nations providing your team’s recommendations on the following: |
| - Your recommendations for allocation of the resources available for HIV/AIDS among ARV provision and a preventative HIV vaccine | - Your recommendations for allocation of the resources available for HIV/AIDS among ARV provision and a preventative HIV vaccine | ||
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| For (1): assume that between now and 2010 the available financial resources could be allocated so as the speed the development of a preventative HIV vaccine – through directly-financing vaccine research and development (R&D), or through other mechanisms. Any gains from such spending would move the date of development you assumed in Task #2 to some earlier date. | For (1): assume that between now and 2010 the available financial resources could be allocated so as the speed the development of a preventative HIV vaccine – through directly-financing vaccine research and development (R&D), or through other mechanisms. Any gains from such spending would move the date of development you assumed in Task #2 to some earlier date. | ||
| - | Here is a zip file which contains a PDF of the problem and all associated data (10) files. (File Size 3MB) | + | Here is a {{mcm-icm: |
2006_年美国大学生数学建模竞赛_mcm_icm_试题.1200137788.txt.gz · 最后更改: 2014/12/30 22:35 (外部编辑)
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