数学建模 美赛 A题.docx

1、数学建模 美赛 A题For office use onlyT1_T2_T3_T4_Team Control Number38915Problem ChosenAFor office use onlyF1_F2_F3_F4_2015 Mathematical Contest in Modeling (MCM) Summary SheetModeling the Impact of Medication on EbolaEbola virus disease is spreading in West African countries. As the medication for Ebola ha

2、s been developed, we manage to offer an optimal plan for controlling the spread of Ebola. At first, we consider the situation without intervention. Based on SEIR model, we formulate an epidemic model (SEIQFR) with time-lag to simulate the future situation of Ebola. Referring to the data from the WHO

3、 early period, we fit the unknown parameters with the least square method. Implementing our model with the data of Sierra Leone, we give a future prediction of Ebola epidemic situation with Runge Kutta method. The result suggests that all compartments become stable in the end, which means an equilib

4、rium point is reached. As for intervention involved situation, we build a non-liner programming model to generate a distribution plan of medication. Based on the first model, we add intervention of vaccine. Assisted with modified Particle Swarm Optimization algorithm, we reach to a solution leading

5、to fewer infected population in Sierra Leone after 4 days with a steady manufacture speed of vaccine. We find the infected people will decrease by 80, therefore proves that vaccine is able to ease the epidemic. Then, we develop a liner programming model to provide a delivery system with the least co

6、st. According to the results in distribution model, we get this solution system for Sierra Leone. Our sensitivity analysis considers influence of other factors. Situations with contact rate changes are tested. The results suggest that the contact rate between infected and susceptible people has the

7、most impact.Our SEIQFR model considers the effect of time-lag, so it suits the features of Ebola better. The model is flexible in infected countries, as long as the initial data of Ebola cases are available.ContentI. Introduction 11.1 Background 11.2 Previous work 11.3 Our work 2II. The Description

8、of the Problem 22.1 How do we simulate future epidemic situation? 22.2 How do we consider the influences of medication distribution? 22.3 How do we analyze our results? 2III. Models 33.1 Notations 33.2 Assumptions 33.3 Improved SEIR Epidemic Model 43.3.1 Ascertainment of the Parameters 63.3.2 Soluti

9、on and Result 73.3.3 Analysis of the Result 93.4 Medication Distribution Optimization Model 93.4.1 Ascertainment of terminology 103.4.2 Solution and Result 113.4.3 Analysis of the Result 133.5 Medication Delivery Model 133.5.1 Solution and Result 14IV. Sensitivity Analysis 154.1Influence of 154.1.1

10、Influence of I 154.1.2 Influence of Q 164.1.3 Influence of F 174.1.4 Analysis of results 174.2 Time begin intervention 17V. Conclusions 185.1 Conclusions of the problem 185.2 Strengths and weaknesses 185.2.1 Strengths 185.2.2 Weaknesses 19VI. Future Work 19VII. References 20VIII. Memo 21I. Introduct

11、ion1.1 BackgroundEbola virus disease (EVD), the disease with most fatality rate, spreads by direct contact withbody fluids, such asblood, of an infected human or other animals. The current outbreak in west Africa, (first cases notified in March 2014), is the largest and most complex Ebola outbreak s

12、ince the Ebola virus was first discovered in 1976. Ebola is not only fatal, but also with high risk of transmission. Even the body of Ebola patients are infectious, so improper burials may also cause infection. Another characteristic of Ebola is the latent period, which possibly varies from 4 to 6 d

13、ays but can top to 29 days long. During the latent period, the infectious has little chance of transmission and appears no symptom.Recently, drugs aiming at curing Ebola patients has been successfully developed. As a world-focusing virus, Ebolas spread situation has been studied for a period of time

14、. The new medicine is a great help to control the epidemic situation. Thus at present, we can assist the Ebola eradication process if optimal plan is proposed, which can be reached by building an mathematical simulation model of the epidemic situation. Furthermore, relevant factors, such as the quan

15、tity of the medicine needed, possible feasible delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug and other possible ones, can also be addressed on the basis of the former model. Among all infected countries, Guinea, Liberia and Sierra Leone are the three most affected ones. And there are still newly occurred cases daily. So every beneficial measurements counts. As long as the method is reasonable and scientific, the adoption of which can be of great impor