2015年美赛A题优秀论文

For office use only

T1 ________________

T2 ________________

T3 ________________

T4 ________________ Team Control Number 35798 Problem Chosen For office use only F1 ________________ F2 ________________ F3 ________________

F4 ________________ A

2015 Mathematical Contest in Modeling (MCM) Summary Sheet

(Attach a copy of this page to your solution paper.)

Farewell to Ebola

Summary

The current outbreak of Ebola has caused great harm to the people in West Africa since it began in December 2013. Fortunately, the world medical association has created new medication to stop Ebola. In this paper, we set up mathematic models in two parts in order to control and even eradicate the Ebola virus disease.

On the one hand, we establish two transmission dynamical models, the medicine model and the medicine-vaccine model, which are based on the basic model of infectious disease. First, we divide people into different types. Then, we build the conversion relationship between different types of people, on basis of which we get the iterative equations. At last, we iterate the equations to obtain the predicting results. We find that the medicine has larger effect on the control of Ebola virus disease than vaccine, because the contact rate is pretty small. Therefore, it is urgent to deliver medicine to the infected districts. Besides, we obtain the optimal maximal quantity of medicine produced every day is 2000 pieces.

On the other hand, we set up two optimal delivery routes for medicine and vaccine separately. The former focuses on the shortest time and it is optimized by the improved Dijkstra Algorithm. The latter concentrates on the least distance and it is optimized by the refined Saving Algorithm. Finally, we conclude that there are 11 trucks required to transport the medicine for 20 days and 7 trucks transporting the vaccine for 30 days when the daily number of vaccine transported is 0.3 million pieces.

Additionally, we analyze the strengths and weaknesses of our models and write a letter for the world medical association to propose our suggestions.

Content

1 Introduction ..................................................................................................................... 3

1.1

1.2

2

3 Analysis of the Problem ............................................................................................. 3 Literature Review ....................................................................................................... 3 Assumptions ..................................................................................................................... 4 The Transmission Model ................................................................................................ 4

3.1

3.2 The Basic Model of Epidemic Dynamics................................................................... 4 The Medicine Model .................................................................................................. 6

3.2.1 Partition of People .................................................................................................. 6

3.2.2

3.2.3

3.2.4

3.2.5

3.3 Assumptions ....................................................................................................... 6 Establishment of the Model ................................................................................ 7 Parameter of the Model ...................................................................................... 9 Result of the Model .......................................................................................... 10 The Medicine-vaccine Model ................................................................................... 11

Assumptions ..................................................................................................... 12

Establishment of the Model .............................................................................. 12

Result of the Model .......................................................................................... 13 3.3.1 3.3.2 3.3.3

4 The Delivery Systems .................................................................................................... 17

4.1

4.2 Collection of Data .................................................................................................... 17 The Delivery Systems for Medicine ......................................................................... 18

Assumptions ..................................................................................................... 18

Establishment of the Delivery systems ............................................................. 18

Result of the Model .......................................................................................... 19 4.2.1 4.2.2 4.2.3

4.3 The Delivery Systems for Vaccine ........................................................................ 20

Assumptions ..................................................................................................... 20

Establishment of the Delivery Systems ............................................................ 20

Result of the Model .......................................................................................... 22 4.3.1 4.3.2 4.3.3

5

6

7

8

Conclusion ...................................................................................................................... 23 Strengths and Weaknesses ............................................................................................ 24 A Letter for the World Medical Association ............................................................... 25 References ......................................................................................................... …… 此处隐藏：19706字，全部文档内容请下载后查看。喜欢就下载吧 ……