HIMCM 2014美国中学生数学建模竞赛

Problem B: The Next Plague?
In 2014, the world saw the infectious Ebola virus spreading in western Africa. Throughout human history, epidemics have come and gone with some infecting and/or killing thousands and lasting for years and others taking less of a human toll. Some believe these events are just nature’s way of controlling the growth of a species while others think they could be a conspiracy or deliberate act to cause harm. This problem will most likely come down to how to expend (or not expend) scarce resources (doctors, containment facilities, money, research, serums, etc…) to deal with a crisis.

在2014年，世界人民看到了感染埃博拉病毒在西非蔓延。纵观人类历史，流行病来了又走，有些流行病杀死了成千上万的人并且持续数百年，另外一些流行病导致少量的人员伤亡的。一些人认为，这些事件只是大自然在控制物种的生长，而其他人则认为，这可能是一个阴谋，或者是故意行为所造成伤害。这个问题很可能会归咎于如何花费（或不花费）稀缺资源（医生，防护设施，资金，科研，血浆等），以应对危机。

Section A:

A routine humanitarian mission on an island in Indonesia reported a small village where almost half of its 300 inhabitants are showing similar symptoms. In the past week, 15 of the “infected” have died. This village is known to trade with nearby villages and other islands. Your modeling team works for a major center of disease control in the capital of your country (or if you prefer, for the International World Health Organization).

A部分：

一个常见的人道主义报道：在印度尼西亚的岛上的一个小村庄，那里的300名居民中几乎有一半都出现了类似的症状。在过去的一周，15个“传染”着已经死亡。这个村与附近的村庄和其他岛屿进行交易而出名。您的建模团队工作的疾病控制的一个主要中心是贵国的首都（或者，如果你喜欢，可以说是国际世界卫生组织）。

Requirement 1: develop a mathematical model that performs the following functions as well as how/when to best allocates these scarce resources and…
- Determines and classifies the type and severity of the spread of the disease
- Determines if an epidemic is contained or not
- Triggers appropriate measures( when to treat, when to transport victims, when to restrict movement, when to let a disease run its course, etc…) to contain a disease.
Note: While you may want to start with the well-known “SIR” family or models for parts of its problem, consider others,

modifications to the SIR, multiple models, or creating your own.

要求1：建立一个数学模型执行以下功能，包括如何/何时最佳分配这些稀缺资源...

- 确定和分类的疾病传播的类型和严重程度

- 或者，确定疫情是否受控（爆发）

- 引发适当的措施（什么时候治疗，什么时候运送受害者，什么时候限制转移，什么时候让疾病听其自然，等等）去控制某种疾病。

注意：此时你可能要开始使用著名的“SIR”模型或该模型的部分，或者考虑别的修正后的SIR模型，多个模型，或者创建自己的模型。

Requirement 2: Based on the information given, your model, and the assumptions your team has made, what initial recommendations does your team have for your country center for disease control? (Given 3-5 recommendations with justifications)

Additional Situational Information: A multi-national research team just returned to your country capital after spending

7 days gathering information in the infected village.

要求2：根据所给出的信息、你的模型以及你的团队所做的假设，你的团队需要为你的国家疾病预防控制中心给出哪些初步建议？（3-5给出建议，理由）

附加态势信息：多国研究小组花7天聚集在村里被感染后的信息返回给你的国家首都。

Requirement 3: You can ask them up to 3 questions to improve your model. What would your ask and why?  
Additional Situational Information: The mulit-national research team concluded that the disease:
-Appears to spread through contact with bodily fluids of an infected person
-The elderly and children are more likely to die if infected
-A nearby island is starting to show similar signs of infection
-One of the researchers that returned to your capital appears infected

要求3：你可以要求问他们3个问题，以改进你的模型。你需要问什么问题和原因？

附加情境信息：多国研究小组得出结论一致认为，本病：

-出现传播是通过与受感染者的体液接触

-如果感染，老人和儿童更容易感染

-附近的岛上开始出现类似感染的迹象

-一个研究者返回到贵国首都出现感染

Requirement 4:How does the additional information above change/modify your model?
要求4：如何根据以上的附加信息改版/修改模型？

Requirement 5:Write a one-page synopsis of your findings for your local non-technical news outlet.

要求5：写下你的发现，为当地的非技术性广播电台(或电视台)提供新闻稿。

更多美赛国赛资料见

数学建模与统计建模论坛

Mathematical Modelling and Statistical Modelling Forum

http://www.mathsccnu.com/forum.php 

4