2015年美赛A题优秀论文

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35798

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A

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2015 Mathematical Contest in Modeling (MCM) Summary Sheet

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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

1Introduction (3)

1.1Analysis of the Problem (3)

1.2Literature Review (3)

2Assumptions (4)

3The Transmission Model (4)

3.1The Basic Model of Epidemic Dynamics (4)

3.2The Medicine Model (6)

3.2.1Partition of People (6)

3.2.2Assumptions (6)

3.2.3Establishment of the Model (7)

3.2.4Parameter of the Model (9)

3.2.5Result of the Model (10)

3.3The Medicine-vaccine Model (11)

3.3.1Assumptions (12)

3.3.2Establishment of the Model (12)

3.3.3Result of the Model (13)

4The Delivery Systems (17)

4.1Collection of Data (17)

4.2The Delivery Systems for Medicine (18)

4.2.1Assumptions (18)

4.2.2Establishment of the Delivery systems (18)

4.2.3Result of the Model (19)

4.3The Delivery Systems for Vaccine (20)

4.3.1Assumptions (20)

4.3.2Establishment of the Delivery Systems (20)

4.3.3Result of the Model (22)

5Conclusion (23)

6Strengths and Weaknesse s (24)

7 A Letter for the World Medical Association (25)

8References (26)