五山湖杯数学建模大赛官方网站
设为首页
 
首 页 | 五山湖 | 数学建模 | 自然现象 | 思想源泉 | 木棉芒果 | 礼品收藏 | 珊瑚礁 | 百步梯 | 联系咨询
  当前位置:首页 > 美国数学建模竞赛 

2006 C - Trade-offs in the fight against HIV/AIDS
发布日期:2011/5/2 16:41:35
 点击:2082
2006 C - Trade-offs in the fight against HIV/AIDS
As the HIV/AIDS pandemic enters its 25th year, both the number of infections and number of deaths due to the disease continue to rise. Despite an enormous amount of effort, our global society remains uncertain on how to most effectively allocate resources to fight this epidemic.
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, and outlines specific tasks.
Task #1: For each of the continents (Africa, Asia, Europe, North America, Australia, and South America), choose the c ountry 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 c ountries 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 s elected the c ountries 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, etc.) and care interventions (treating other untreated sexually transmitted diseases, treating opportunistic infections, etc.). You should focus on only two potential interventions: provision of antiretroviral (ARV) drug therapies, and provision of a hypothetical HIV/AIDS preventative vaccine.
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  c ountries you s elected 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 s elected c ountries 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.
You can choose whether these scenarios should be implemented for all of the c ountries you s elected in Task #1, or for certain subsets of c ountries based on income cut-offs, disease burden, etc. Available for use if you wish is a spreadsheet of c ountry-level income data.
ARV drug therapies can have tremendous benefits in terms of prolonging the lives of individuals infected with HIV/AIDS. ARVs are keeping a high proportion of HIV/AIDS-infected individuals in rich c ountries alive, and policy makers and international institutions are facing tremendous political pressure to increase access to ARVs for individuals in poor c ountries. Health budgets in low-income c ountries are very limited, and it seems unlikely that poor c ountries will be able to successfully expand these programs to the majority of their populations using their own resources. Appendix 1 presents c ountry-specific data from UNAIDS on current access to ARVs for a number of c ountries
The efficacy of ARVs depends in large part on adherence to the treatment regimen and to proper monitoring. The most favorable conditions for ARVs are structured programs with extensive counseling and physician care, as well as regular testing to monitor for disease progression and the onset of opportunistic infections. Non-adherence or inadequate treatment carries with it two very serious consequences. First, the treatment may not be effective for the individual undergoing treatment. Second, partial or inadequate treatments are thought to directly lead to the emergence of drug-resistant strains of HIV.
The price of the drugs initially used to treat patients has come down to several hundred dollars a year per patient, but delivering them and providing the necessary accompanying medical care and further treatment is the key administrative and financial challenge. It is estimated that purchasing and delivering antiretrovirals using the clinically-recommended approach (DOTS, or directly observed short course treatments) which is intended to minimize the emergence of drug-resistant strains would cost less than $1,100 per person per year. (Adams, Gregor et al. [2001]. “Consensus Statement on Antiretroviral Treatment for AIDS in Poor C ountries,”)
For a preventative HIV vaccine, make assumptions you feel are reasonable about the following (in addition to other factors you may choose to include in your model):
  1. The year in which an HIV/AIDS preventative vaccine might be available
  2. How quickly vaccination rates might reach the following steady-state levels of vaccination:
    1. If you wish to immunize new cohorts (infants), assume the steady-state level for new cohorts of the c ountry-by-c ountry immunization rates for the third dose of the diphtheria-pertussis-tetanus vaccine (DTP3), as reported by the WHO (2002)
    2. If you wish to immunize adults (any group over age 5), assume the steady-state level for older cohorts is the second dose of the tetanus toxoid (TT2) rate, as reported by the WHO (2002)
  3. The efficacy and duration of protection of the vaccine
  4. Whether there would be epidemiological externalities from vaccination
  5. 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.
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.
Second- and third-line ARV drug therapies are available, but assume for your analysis that these drugs are prohibitively expensive to implement in c ountries 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:
  1. Your recommendations for allocation of the resources available for HIV/AIDS among ARV provision and a preventative HIV vaccine
  2. Your argument for how to weigh the importance of HIV/AIDS as an international concern relative to other foreign policy priorities
  3. Your recommendations for how to coordinate donor involvement for HIV/AIDS
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)
 
收 藏 推 荐 打 印 关 闭


最新录入  
 · 2019年广东省工业与应用数...
 · 第一届“百农杯”数学建模竞赛...
 · A Microcircuit...
 · Burst firing t...
 · 第二届全国神经动力学会议回执
 · 第二届全国神经动力学会议论文...
 · 第二届全国神经动力学会议征文通知
 · 第二届全国神经动力学会议学术...
 · 第二届全国神经动力学会议(第...
 · 第二届全国神经动力学会议
相关内容   更多>>
 · 2011 ICM Problem
 · 2011 MCM Probl...
 · 2011 MCM Probl...
 · 2010 C: The Gr...
 · 2010 MCM PROBL...
 · 2010 MCM PROBL...
 · 2009 ICM C: Cr...
 · 2009 MCM PROBL...
 · 2009 MCM PROBL...
 · 2008 C: Findin...
 
声明 | 报名须知 | 联系方式 | 五山湖 技术支持:郑州建网站 Copyright (c) 2011 All Rights Reserved.