2015MCM 赛题点评 A

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magic2728

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	慵懒 2014-9-29 19:37

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群组: 数学中国 2015美赛护航

群组: 数模专题强化培训

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发表于 2015-4-25 16:52 |只看该作者 |倒序浏览

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由于工作原因，迟迟没时间把今年美赛题目的点评贴放上，直到大家都开始晒成绩，网络挑战赛又进行得如火如荼，才把尘封已久，在比赛指导期间完成的美赛点评贴作一修改后上传，仍然沿用函数建模法，仍然沿用信息标注法，仍然是那三种更古不变的模型贯穿始终。希望通过这些分析，让大家看到数学建模的本质，甚至是科研的本质，项目的本质，真的提升自己的理解力。
首先是标准优化问题压阵，带着一点点预测的工具手段，少不了一点点的评价，大家可以想想，此题难度在哪里，哪里需要我们下更多的功夫？

PROBLEM A: EradicatingEbola(bk1)

The world medicalassociation has announced that their new medication could stop Ebolaand cure patients whose disease is not advanced.(bk2)

Build a realistic,sensible, and useful(imp1) model(spm1) that considers not only the 1. spread of thedisease, 2. the quantity of the medicine needed, 3. possible feasibledelivery systems, locations of delivery, 4.speed ofmanufacturing of the vaccine or drug（rsc1）, but also any other criticalfactors(imp2) your team considers necessary as part of the model to optimize the eradicationof Ebola, or at least its current strain.

In addition toyour modeling approach for the contest, prepare a 1-2 page non-technical letter for the worldmedical association to use in their announcement.（mss1）

It is a canonical optimization question inthe background of social problem as presented in the 2nd sentence,which we can execute the routine of solving optimization problem and do more ofstatistics as the modeling tool, also don't forget the mechanism analysis,noting the restrictive conditions and implications noted above. Below is thecritical element I believe, only for reference:

1. decision variable: delivery schedule(including system, locations and etc.) and other factors(foods, comfort and etc…which is executable);

2. objective: eradication of Ebola, can bequantified as the minimal time to obtain the steadiness or removing it, ormaximal speed of delivering the drugs;

3. parameters (cannot be controlled andneed to do sensitivity analysis): initial number of diseased people(x, mayinclude its space distribution), speed of spreading(v1), speed of producingdrugs(v2);

4. objective function: we must simulatethe process of the spreading of disease and the effect of the drugs against it,cellular automation to discrete space and time to dynamically describe theprocess, or you can solve it by differential equations. The second part is thedelivering schedule, and queueing theory can be used to consider the servicepart of it.

Pleaseignore the minor factors and I believe grasp 'spreading simulation' and'delivering service' are 2 key point of the model, good luck!