2015年美赛O奖论文A题Problem_A_35532pdf.doc

Team Control Number For office use only 35532 For office use only T1 ________________ F1 ________________ T2 ________________ F2 ________________ T3 ________________ Problem Chosen F3 ________________ T4 ________________ F4 ________________ A 2015 Mathematical Contest in Modeling (MCM) Summary Sheet Summary The complex epidemic of Zaire ebolavirus has been affecting West Africa. A series of realistic, sensible, and useful mathematical model about Ebola of spreading and medication delivery are developed to eradicating Ebola. 这个复杂的传染病，埃博拉，已经影响西非好久。一系列真实可信的关于抑制埃博拉传播和医药相关的数学模型正在建立。 First, we divide the spreading of disease into three periods: naturally spreading period, spreading period with isolation but without effective medications and spreading period with effective medications. We develop a SEIR (susceptible-exposed-infectious-recovered) model to simulate the spread of the disease in the primary period. Then the model are improved to a SEIQR (susceptible-exposed-infectious-quarantined-recovered) model to adapt to the second and third period and to predict the future trends in 第一，我们把这个疾病划分为三个部分：自然传播过程，没有有效药物控制的独立传播过程和有有效控制的传播过程。我们建立了一个SEIR（易受暴露的感染性恢复）模型来模拟早期疾病的传播。接着我们又把模型升级为一个SEIQR（易受暴露性感染后的隔离恢复）来适应第二和第三阶段的传播同时也用来预测在Guinea, Sierra Leone and Liberia.的传播情况。 According to our plan, drugs are delivered to countries in need separately by air, then to medical centers by highway and be used for therapy of patients there. To solve the problem of location decision of medical centers, which belongs to a set covering problem, we developed a multi-objective optimization model. The model’s goal is minimizing the numbers of medical centers and total patients’ time cost on the road on the condition that all of patients can be sent a medical center in time. We solved the model with genetic algorithm, and get an approximate optimal solution with 7 medical centers. 根据我们的计划，运送药物的国家个别的需要空中运输，然后疾病中心通过高速公路将药物运送到患者手中。为了决定当地医疗中心位置的一个覆盖问题，我们建立了一个多元线性规划的选择