国际数学建模竞赛优秀论文英文模板中学教育竞赛题_中学教育-竞赛题.pdf

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1、国际数学建模竞赛优秀论文英文模板 1/38 Team Control Number For office use only 38253 For office use only T1 F1 T2 F2 T3 Problem Chosen F3 T4 A F4 2015 Mathematical Contest in Modeling(MCM)Summary Sheet Eradicating Ebola Abstract This paper aim at the problem which is to eradicate or inhibit the spread of Ebola,we st

2、art from three sub problem,that is:the demand for drugs,drugs delivery route and the car allocation.And establish the spreading model of Ebola,optimization model of drugs transport system and car allocation model respectively by using the differential equation method and simulated annealing algorith

3、m.Finally,do the model extension and sensitively analysis.The first issue,figure out the demand for drugs in different regions.First,establish Ebola spread SIR model.And in the time of t,using differential equation to find the proportion of infected i(t)=1/Qln(s/s0),then get the demand for drugs in

4、this region H=kNi(t).The second issue,how to find the shortest route to deliver drugs.Use Guinea,Liberia and Sierra Leone whose infection is relatively serious as the investigation object.According to the Binary classification to find the rules of iteration,which 国际数学建模竞赛优秀论文英文模板 2/38 is useful to f

5、ind out the nearest city to any other cities,and the result is Bombali.So we put it as the center of distribution.Then use simulated annealing algorithm and put forward two kinds of schemes for shortest path by the different ways in drugs delivery.Schemes one,asynchronous mode:put three countries as

6、 a regional countries.Using the TSP method to solve the shortest route is 54.8486,which is start from Bombali to different regions.Schemes two,synchronization method:dividing the whole area into two areas around A and B by use the longitude coordinates of Bombali as a standard.Respectively solve the

7、 shortest route is 10.1739 and 29.8075,which is start from Bombali and pass all cities in A and B,and solve the sum of the two route is 39.9814.According to the different drug delivery requirements(such as the shortest distance or transmission synchronization),can choose the asynchronous or synchron

8、ous way.The third issue,how to allocate the number of cars reasonable,and obtain the suitable speed of drug production.According to the predict number which obtained in model one,get the vehicles and drug distribution table(the results are shown Table 4.6 and Table 4.7).and obtain the speed V of dru

9、gs production is:10(lnln)niiiiiik NVQTss At last,the minimum speed of drugs production is 56.14 agent/day to meet the need in three countries by calculating.Finally,use the SIR model which was optimized by using vaccination cycle control.By doing this we can know the number of susceptible and infect

10、ions in crowd under the condition of the pulse vaccination significantly lower faster than without pulse vaccination.Thus,using pulse vaccination can effectively control the spread of Ebola.Keywords:SIR model;Simulated Annealing Algorithm;Pulse vaccination;Ebola 际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模

11、竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 3/38 Eradicating

12、Ebola Content 1 Restatement of the Problem.1 1.1 Introduction.1 1.2 The Problem.1 2 General Assumptions.2 3 Variables and Abbreviations.3 4 Modeling and Solving.4 4.1 Model I.4 4.1.1 Analysis of the Problem.4 4.1.2 Model Design.4 4.2 Model II.10 4.2.1 Analysis of the Problem.10 4.2.2 Model Design.11

13、 4.3 Model .16 4.3.1 Analysis of the Problem.16 4.3.2 Model Design.17 4.4 Extent our models.23 5 Sensitivity Analysis.27 5.1 Effect of Daily Contact Rate.27 5.2 Effect of inoculation rate.28 际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模

14、板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 4/38 6 Model Analysis.29 6.1 The Advantages of Model.29 6.2 The Disadvantages of Model.30

15、 7 Non-technical Explanation.31 References.34 际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国

16、际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 1/38 1 Restatement of the Problem 1.1 Introduction Ebola virus is a very rare kind of virus.It can cause humans and primates produce Ebola hemorrhagic fever virus,and has a high mortality rate.The largest and most complex Ebola outbre

17、ak appeared in the West African country in 2014.This outbreak occurred in guinea first,then through various ways to countries such as Sierra Leone,Liberia,Nigeria and Senegal.The number of cases and deaths,which occurred in this outbreak,is more than the sum of all the other epidemic.And outbreak co

18、ntinued to spread between countries.On August 8,2014,the general-director of the world health organization announced the outbreak of public health emergency of international concern.In this paper,a realistic and reasonable mathematic model,which considers several aspects such as vaccine manufacturin

19、g and drug delivery,has been built.Then optimizing the model to eliminate or suppress the harm done by the Ebola virus.1.2 The Problem Establishing a model to solve the spread of the disease,amount of drugs needed,possible feasible transportation system,transporting position,the speed of a vaccine o

20、r drug manufacturing and any other key factor.Thus,we decompose the problem into three sub-problem,际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论

21、文文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 2/38 modeling and finding the optimization method to face the Ebola virus.Building a model,which can solve the spread of the disease and the demand for drugs.Building a model to fin

22、d the best solution.Using the goal programming to solve the problems of production and distribution and optimization of other factors.2 General Assumptions To simplify the problem,we make the following basic assumptions,each of which is properly justified.Our assumptions is reasonable and effective.

23、Vehicles only run in the path which we have simulated This assumption greatly simplify our model and allow us to focus on the shortest path.We consider the model that are enclosed.People who recovered,will not infected again,and exit the transmission system 际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论

24、文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 3/38 3 Variables and A

25、bbreviations The variables and abbreviations used in this paper are listed in Table 3.1.Table 3.1 Assuming variable Symbol Definition S the number of susceptible people I the number of infected persons R the number of recovered T a vaccine or drug production cycle H the amount of drugs needed by Reg

26、ion A a cycle of a vaccine or drug production L drug reserve area to the shortest path to all affected areas V speed of vaccine or pharmaceutical production V vehicle speed rate of patient contact per day day cure rate per day n rights of those infected regions weight 际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板

27、国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 4/38 4 Mode

28、ling and Solving 4.1 Model I 4.1.1 Analysis of the Problem According to the literature that different types of virus has its own different propagation process characteristics,we do not analyze the spread of viruses from a medical point of view,but from the general to analyze the propagation mechanis

29、m.So we have to analyze the spread of the Ebola virus and the requirements of drugs through the SIR1 model.4.1.2 Model Design In the dynamics of infectious diseases,the main follow Kermack and McKendrick SIR epidemic model which the dynamics of the established method in 1927.SIR model until now is s

30、till widely used and continue to develop.SIR model of the total population is divided into the following three categories:susceptibles,the ratio of the number denoted by s(t),at time t is not likely to be infected,but the number of infectious diseases such proportion of the total;infectives,the rati

31、o of the number denoted by i(t),at time t become a patient has been infected and has the proportion of the total number of contagious;recovered,the ratio of the number denoted by r(t),expressed the number of those infected at time t removed from the total proportion(ie,it has quit infected systems).

32、Assuming a total population of 际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板

33、国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 5/38 N(t),then there are N(t)=s(t)+i(t)+r(t).SIR model is established based on the following two assumptions:In the investigated region-wide spread of the disease is not considered during the births,deaths,population mobility and other dynamic facto

34、rs.Total population N(t)remain unchanged,the population remains a constant N.The patients contact rate(the average number of effective contacts per patient per day)is constant,the cure rate(patients be cured proportion of the total number of patients a day)is a constant,clearly the average infectiou

35、s period of 1/,infectious period contact number for Q=/.In the model based on the assumption that we develop a susceptible person to recover from the sick person in the process,such as Figure 4.1:sir Figure 4.1 SIR the model flowchart SIR basis differential equation model can be expressed as:disiidt

36、dssidtdridt (5.1)But it can see that s(t),i(t)is more difficult to solve,so we 际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文文模板国际数学建模竞赛优秀论文英文模板

37、国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 6/38 use the numerical calculations to estimate general variation.Assuming =1,=0.3,i(0)=0.02,s(0)=0.98(at the initial time),then we borrow MATLAB software programming to get results.And according to Ta

38、ble 4.1 analyzed i(t),s(t)of the general variation.Table 4.1 Assuming variable t i(t)s(t)t i(t)s(t)0 0.02 0.98 9 0.2863 0.1493 1 0.039 0.9525 10 0.2418 0.1145 2 0.0732 0.9019 15 0.0787 0.0543 3 0.1285 0.8169 20 0.0223 0.0434 4 0.2033 0.6927 25 0.0061 0.0408 5 0.2795 0.5438 30 0.0017 0.0401 6 0.3312

39、0.3995 35 0.0005 0.0399 7 0.3444 0.2839 40 0.0001 0.0399 8 0.3247 0.2027 45 0 0.0398 0510152025303540455000.10.20.30.40.50.60.70.80.91s(t)i(t)00.10.20.30.40.50.60.70.80.9100.050.10.150.20.250.30.35 际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛

40、优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 7/38 Figure4.2 s(t),i(t)The patient scale map Figure 4.3 is Phase track diagram Fr

41、om Table 4.1 and Figure4.2,we can see that i(t)increased from the initial value to about t=7(maximum),and then began to decrease.Based on the calculating the numerical and graphical observation,use of phase trajectories discussed i(t),s(t)in nature.Here i s plane is phase plane,the domain(s,i)D in p

42、hase plane for:(,)0,0,1Ds i sisi (5.2)According to equation(5.1)and contact number of the infectious period Q=/,we can eliminate dt,get:0011(1)(1)isisssdidsdidsQQ (5.3)Calculated using integral characteristics:0001()()lnsi tsisQs (5.4)Curve in the domain of definition,equation(5.3)is a phase traject

43、ory.According to equation(5.1)and equation(5.3),have to analyze the changes.If and only if the patient i(t)for some period of growth,it think that in the spread of infectious diseases,then 1/Q is a threshold.If s0 1/Q,infectious diseases will spread,and reduce infectious period the number of contact

44、s with Q,namely raising the threshold 1/Q and will make s01/Q,then it will not spread diseases.际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文文模板

45、国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 8/38 And we note that Q=/in the formula,the higher the level of peoples health,the smaller patients contact rate;the higher the level of medical,the cure rate is larger and the smaller

46、Q.Therefore,to improve the level of hygiene and medical help to control the spread of infectious diseases.Of course,can also herd immunity and prevention,to reduce s0.In the process,we analyzed the spread of the disease,then we are going to discuss the amount of medication needed.According to equati

47、on(5.4),you can get i(t)values,we can calculate the number of people infected with the disease who I was:()()Ii tN t (5.5)And the amount of drug required,we can be expressed as:HkI(k is a constant,w 0)If k 0,it indicates that the number of infections is still rising,measures to control the virus als

48、o needs to be strengthened,and the amount of drugs is a growing demand mode until fluctuation;if k0,it means reducing the number of people infected,the virus the measure is better,and the dose of demand is also gradually reduced.According to the data provided by the WHO,we can get the number of infe

49、ctions various，which areas before January 30,2015.see Table 4.2:Table 4.2 As the number of infections January 30,2015 际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛

50、优秀论文英文模板国际数学建模竞赛优秀论文文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际数学建模竞赛优秀论文英文模板国际国际数学建模竞赛优秀论文英文模板 9/38 Region Number Proportion Region Number Proportion Nzerekore 2 0.0045 Koinadugu 1 0.0022 Macenta 1 0.0022 Kambia 25 0.0558 Kissdougou 1 0.0022 Western Urban 1