数学建模美赛O奖论文

Team Control Number For office use only T1 T2 T3 T4
34103
Problem Chosen
For office use only F1 F2 F3 F4
A
2015 Mathematical Contest in Modeling (MCM) Summary Sheet
Model 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 The model description . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . Model Establishment . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Team #34103 February 10, 2015
Team # 34103
Page 3 of 34
Contents
1 Introduction 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The Description of Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 1.2.2 2 3 4 What problems we are confronting . . . . . . . . . . . . . . . . . . . What we do to solve these problems . . . . . . . . . . . . . . . . . . 5 5 5 5 5 6 6 7 7 7 7 8 8 9 11 12 12 12 12 13 14 15 16 16 17 17 17 18 19 19 19 20 20 20
4.3
Model 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 The model description . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . Model Establishment . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4
Model 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 The model description . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 4.4.3 4.4.4 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . Model Establishment . . . . . . . . . . . . . . . . . . . . . . . . . . .
Concerning the natural transmission of Ebola, an infection disease model is built by the method of ODE (Ordinary Differential Equation).This model estimates the tremendous effects of Ebola in the absence of effective prevention and control measures. With consideration of effective vaccine and medicine, this paper simulates the prevention and control measures against Ebola in the case of sufficient medicine, by modifying the SIQR (Susceptible Infective Quarantine Removed) model. For the problem of transporting the vaccine and medicine, we use the method of MST (Minimum Spanning Tree) to reduce the overall cost of transportation, set the time limit and security points and form a point set of the target areas where the security points, as transit stations, can reach within a limited period of time. And then we use BFS (Breadth-First Search) to search every program which can cover all the points with minimal transfer stations and assign points to their nearest transfer stations to distribute the medicine. This program has taken cost, time and security during the transportation into consideration, in order to make analysis of the optimal solution. Then with the help of the modified SIQR model, the development of epidemic situation in the whole area can be predicted under the circumstance that vaccine quantity supplied in a supply cycle is determined. Thus a treatment evaluation system is established through calculating the actual mortality rate. On the other hand, vaccine quantity demanded in a supply cycle could be calculated when a certain mortality rate is expected. In the end of this paper, the other factors which may have impacts are considered too, in order to refine the model. And the future works are proposed. In conclusion, four models are established for controlling Ebola. Epidemic situation development are predicted under different circumstances firstly. Then we built a medicine delivery system for transferring medicine efficiently. Based on these, death rate and vaccine quantity demanded could be calculated.
Abstract Ebola epidemic can be controlled if a comprehensive prevention and control system can be established. This paper makes quantitative analysis for the prevention and control of Ebola.
Keywords: Ebola; infection model; optimal solution; evaluation system
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Team # 34103
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Evaluation system based on Ebola’s prevention and medecine’s delivery system
Terms and Definitions Basic Assumptions Models 4.1 Model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 The model description . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 4.2 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . Model Establishment . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .