2019美赛特等奖全部论文c1922154

1、添加微信 math-o 获取免费课程For office use onlyF1 F2 F3 F4 请关注“校苑数模”微信公众号，获取更多资Te料am Control Number For office use only1922154Problem ChosenCT1 T2 T3 T4 2019MCM/ICMSummary SheetThe Current Status, Future and Strategy of OpioidSummaryThe United States is experiencing a crisis regarding the abuse of opioids whi

2、ch poses a great threat to the development prospects of the United States. Based on the idea of cellular automata, we not only describe the spread and characteristics of reportedsynthetic opioid andcases in Ohio, Kentucky, West Virginia, Virginia, andPennsylvania, but also develop a possible strateg

3、y countering the opioid crisis.We define a county and the nearest k counties around it as an “environment”. Based on the idea of KNN, we determine the m “environments” that are most similar to the “environment” of the county, and then use the cellular automata to predict the number of cases in the c

4、ounty next year with the growth rate of m “environments”. At the same time, we define the opioid incidents concentration index (CI) to characterize the degree of aggregation of cases by reference to the HHI index. Finally, we obtain the distribution ofsynthetic opioids andincidents in five states. C

5、ases are still concentrated intransportation hubs and there is a tendency to spread.spread to the southwest inKentucky with Lexington as the center and has a tendency to spread throughout Pennsylvania and Virginia. Based on historical data and prediction, we determine the drug identification thresho

6、ld levels for each state. In 2026, Ohio will reach its threshold of 120,000, making it difficult for the government to control the amount of opioid use and the speed of spread.In order to determine whether certain socio-economic factors have a significant impact on the trend of opioid usage, we sele

7、ct the first 25% and the last 25% of the data for all state cases in 2010-2016 for analysis of variance if the data passes the test of variance homogeneity. Correlation analysis is performed on data that do not pass the test for variance homogeneity to determine the correlation between socio-economi

8、c factors and trends in opioids usage. The final selection of significant factors is marital status, educational attainment, ancestry, and language spoken at home. Adding the important factors selected above to the “environment” similarity considerations, we have obtained a modified model that consi

9、ders socio-economic factors.Based on the above analysis, we develop a strategy contains two actions for dealing with opioid crisis. The first one is giving couples a discount on tax and mortgage rates to encourage people to marry at legal age. The other is opening a low-cost English language trainin

10、g institution to improve the English proficiency of non-native English speakers.Key words: Opioid; Cellular automata; Concentration index; Spread; Characteristics校苑数模收集整理，版权归原作者所有请关注“校苑数模”微信公众号，获取更多资料 添加微信 math-o 获取免费课程MEMOFrom: Team # 1922154 To: Chief Administrator Data: January 27, 2019Subject: H

11、ow to deal with the opioid crisisDear chief administrator, we are honored to inform you our achievement after performing data analysis and modeling.First, we introduce the spread and characteristics of synthetic opioid andusagebetween the five states and their counties from 2010 to 2017. Combining t

12、he provided data with the collected latitude and longitude data, we notice that the aggregation point of opioid incidents is mainly in the areas with developed traffic, and there is a tendency to spread around. The distribution of synthetic opioid in Virginia is the most extensive,moreover, the dist

13、ribution in Pennsylvania is the most concentrated. tendency to spread. However, perhaps for some reason, this trend hasonce had a been arrested.Nowadaysis spreading again in some states, such as Virginia.Then, we forecast the synthetic opioid andusage in each county from 2017 to2026. According to th

14、e prediction, synthetic opioids will spread throughout Kentucky in the future. And the synthetic opioids usage of counties around Washington is growing from the forecasting.Based on our observation on provided data and Calculated data, we think about theU.S. government is concern about two points:Th

15、e opioid usage should be restricted to a certain level.The spread of the opioid should be controlled within a certain range.According to the historical data and prediction, we can identify the drug identification threshold levels to predict when and where the governments concern will occur. For exam

16、ple, the threshold level of Ohio is 120,000. governments concern has occurred in Ohio in 2026.By analyzing the Census socio-economic data, we notice that some important variables such as marital status, educational attainment, ancestry and the language spoken will impact on the use of the opioid in

17、each county.Based on the above analysis, we propose a strategy that includes two actions.Give couples a discount on tax and mortgage rates to encourage people to marry at legal age.Open a low-cost English language training institution to improve the English proficiency of non-native English speakers

18、.Our strategy can effectively reduce opioid use.By taking the action 1, the opioid cases will reduce from 257496 to 231073 By taking the action 2, the opioid cases will reduce from 257496 to 225873.The above is the summary of our study. We sincerely hope that it will provide you with useful informat

19、ion.Thanks!校苑数模收集整理，版权归原作者所有请关注“校苑数模”微信公众号，获取更多资料 添加微信 math-o 获取免费课程Contents1 Introduction11.1 Background11.2 Planned Approach12 Terminology, Symbols and Assumptions22.1 Terms22.2 Symbols22.3 General Assumptions33 Spread and Characteristics of Opioid Incidents33.1 Preprocess Data33.1.1 Missing value

20、 processing33.1.2 Geographic coordinate acquisition43.1.3 Overview of drug cases distribution43.2 Spread of Opioid Incidents base on CA Model43.2.1 Introduction to the idea of method43.2.2 Attributes of a Cell53.2.3 Self-defined Rules53.2.4 Concentration index (CI)73.3 Results & analysis73.3.1 Sprea

21、d and Characteristics73.3.2 Concern and Occur93.4 Sensitivity analysis of model104 Model Modification Considering Socio-economic Factors114.1 Preprocess Data114.1.1 Data overview114.1.2 Data selection & Analysis124.2 Important factor selection124.2.1 The general idea of factors selection124.2.2 Grou

22、ping124.2.3 Twofold filter134.3 Model Modification144.4 Results & analysis144.5 Model Evaluation164.6 Strategy174.6.1 Principles of strategy174.6.2 Action175 Strength and Weakness185.1 Strength185.2 Weakness186 Conclusion187 References19Appendix20校苑数模收集整理，版权归原作者所有请关注“校苑数模”微信公众号，获取更多资料 Team # 1922154

23、添加微信 math-o 获取免费课程Page 1 of 201 Introduction1.1 BackgroundAt present, the phenomenon of addiction and abuse of opioids in the United States is serious. The abuse of opioids not only imposes a heavy economic burden on the US government, but also affects the quantity and quality of the US workforce an

24、d the prospects for the US economy. The DEA/National Forensic Laboratory Information System (NFLIS) of the Drug Enforcement Administrations (DEA) Office publishes an annual report on drug identification results and associated information from drug cases. Specifically, they need:a description of the

25、spread and characteristics of synthetic opioids andevents reported between five states and their counties over time and identify possible locations where specific opioids may have begun to be used in five states.an analysis of important factors affecting the use or use of opioids in socio- economic

26、data from the US Census.a possible strategy for countering the opioid crisis.A large amount of literature tracks the abuse of opioids in the United States: for example, Cicero, Inciardi, and Muoz 1 specifically described the t rend of abuse of opioids in the United States from 2002 to 2004 based on

27、the Researched Abuse, Diversion and Addiction-Related Surveillance (RADARS) system; Volkow, Jones, Einstein, and Wargo 2 analyzed the factors that triggered the opioid crisis and its further evolution, as well as interventions to manage and prevent opioid use disorders.However, most of the literatur

28、e does not scientifically summarize its propagation patterns and distribution characteristics over time based on the data of the opioid drug identification cases in various counties, so that the future predictions cannot accurately indicate the time and place where a drug identification may be trans

29、mitted. In addition, past work has not been able to propose effective strategies to deal with the opioid crisis.1.2 Planned ApproachBased on the above analysis, we propose the framework model shown in Figure 1, which can be summarized as the following steps:Characteristics and SpreadDraw heat maps a

30、nd other visualizations using NFLIS data and geographic data(latitude and longitude), and analyze the spread and characteristics of the reportedsynthetic opioid and over time.incidents in and between the five states and their countiesCellular Automata ModelWith the idea of cellular automata which is

31、 the state of the next moment is determinedby the surrounding and its own state, a new cellular automata model is constructed by combining the ideas of clustering and KNN. This model will fully exploit the information of historical data to achieve a more accurate simulation.校苑数模收集整理，版权归原作者所有请关注“校苑数模

32、”微信公众号，获取更多资料 Team # 1922154添加微信 math-o 获取免费课程Page 2 of 20Analyze Socio-economic FactorsWe plan to use statistical one-wayANOVA and correlation analysis to findsocioeconomic factors that have a significant impact on the model and to correct the model.Identify a Possible StrategiesWe will consider th

33、e results of the cellular automata model and the influential socio-economic factors of the analysis, and then develop a possible strategy for countering the opioid crisis. The model will also be used to verify the effectiveness of the strategy.Figure 1: Model framework2 Terminology, Symbols and Assu

34、mptions2.1 TermsOpioids3: medically they are primarily used for pain relief, including anesthesia and they are also frequently used non-medically for their euphoric effects or to prevent withdrawal.4: an opioid most commonly used as a recreational drug for its euphoriceffects. It is generally illega

35、l to make, possess, or sellwithout a license.HHI5: the Herfindahl-Hirschman index is a statistical measure of concentration. For example, it can be used to measure the market concentration. It is calculated by squaring the market shares of all firms in a market and then summing the squares.2.2 Symbo

36、lsTable 1: Variable description校苑数模收集整理，版权归原作者所有SymbolDefinitionThe ith countyThe environment(vector) related to ith county in the nth year The growth rate of opioid usage in the ith county in the nth year请关注“校苑数模”微信公众号，获取更多资料 Team # 1922154添加微信 math-o 获取免费课程Page 3 of 20The error inyear when the val

37、ue of parameters are k and m(,)CIMS EA ANLSThe concentration index Marital status Educational attainment AncestryLanguage spoken at home2.3 General AssumptionsAssumption 1: The change in the number of a county opioid incidents is greatly affected by the surrounding counties, and the historical data

38、can reflect the development of opioids to a certain extent.Reason: This assumption was made to ensure the validity of the cellular automata model we constructed.Assumption 2: The government will not have excessive rectification of opioids from now until 2026, and the changes in the opioids of each c

39、ounty will follow the historical law of 2010-2017.Reason: The reason for this assumption is to ensure the validity of the results predicted by the model to some extent.Assumption 3: The data used in this paper is realistic and accurate to a certain degree. Reason: Although the data is incomplete and

40、 there are some tolerable errors in the statistics, we make this assumption to ensure an effective solution.Assumption 4: Counties, which are not involved in NFLIS Data is not considered in our model.Reason: We believe the counties not involved in NFLIS Data are of little significance to the problem

41、 studied3 Spread and Characteristics of Opioid Incidents3.1 Preprocess Data3.1.1 Missing value processingThe first file (MCM_NFLIS_Data.xlsx) contains most of the countys drug identification counts in year 2010-2017, but some counties still have missing data for a certain year or even years. We susp

42、ect that the county has a drug identification count in the absence of these years, but the name of the drug identified cannot be determined. Therefore, we fill in the missing value of variable County total count of all substances identified as follows:校苑数模收集整理，版权归原作者所有请关注“校苑数模”微信公众号，获取更多资料 Team # 19

43、22154添加微信 math-o 获取免费课程Page 4 of 201 + +1 =(1)2where indicates the missing total count of all substances identified in the county iniththeyear,1indicates the total count of all substances identified in the previousyear,+1indicates the total count of all substances identified in the following year.No

44、tes: If the county has more than three missing data, we believe that the county data is invalid. We give up filling in missing values and abandon them.3.1.2 Geographic coordinate acquisitionIn order to see the geographical distribution of the submitted cases, we obtained five states: the latitude an

45、d longitude data of all counties in Ohio, Kentucky, West Virginia, Virginia, and Pennsylvania from the United States Cities Database website 6. And then we calculate the distance between each county using the Haversine formula 7. Supposethe latitude and longitude of the two counties are (1,1) and (2

46、, 2), respectively.2 12 1) = 2 ( ( 22) + 1 2 (2)22where d is the distance between the two counties, r is the radius of the earth.3.1.3 Overview of drug cases distributionWe draw heat maps using the latitude and longitude data of each state and the data ofdrug identification counts for narcotic analg

47、esics (synthetic opioids) andin eachof the five states, to have a general understanding of the distribution of reported cases.Take the case reported in 2010 as an example (shown in Figure 2). It can be roughly seen from the heat map that the proportion in the transportation hubs and along the lake a

48、nd coastal areas is high.Figure 2: Distribution of drug identification cases in 20103.2 Spread of Opioid Incidents base on CA Model3.2.1 Introduction to the idea of methodTo help us understand the spread of opioid usage between the five states and their counties in the past, we propose a model to si

49、mulate the use of opioids over the past eight校苑数模收集整理，版权归原作者所有请关注“校苑数模”微信公众号，获取更多资料 Team # 1922154添加微信 math-o 获取免费课程Page 5 of 20years in various regions. The simulation results of the model are then used to identify any possible locations in five states that may have begun to use a specific opioid.B

50、ased on the analysis of the problem and data, we summarize the following challenges:The model should be able to reflect the interaction between the use of opioid each county.The model should be able to reflect the impact of the historical development of each county on its future.Models must be able

51、to simulate changes in the number of opioid cases in all counties.In view of these challenges, we adopt the Cellular Automata 8 (CA), a grid dynamics model, in which time, space, and state are all discrete and have the ability to simulate the evolution process of complex systems. Cellular Automata i

52、s a widely used model to analyze the spread problems 9. In this case, the map is divided into cells, and each county occupies a separate cell. A cell records the total drug reports of the county. The state of the cell update based on its current state and the current state of the surrounding cells.

53、We apply the self-defined update rules to simulate the evolution of each countys opioid usage in our model.3.2.2 Attributes of a CellIn our model, each cell can only represent at most one county. A cell has 3 attributes:An integer c (0 or 1) to represent the cell status, 0 for no county, 1 for one c

54、ounty Current number of opioid cases in the county .The rate of change in the number of opioid cases in the county that year The other two properties only make sense when c is non-zero. In each step of the simulation, is updated by the . Self-defined rules are introduced in following sections.3.2.3

55、Self-defined RulesThe key to the cellular automata that can be used to describe the use of opioids in each county is to develop rules that are close to reality. In this case, we develop update rules based on given historical data.First we calculate the distance between them by the latitude and longi

56、tude of each county. Then we take each county and its nearest counties as a set of vectors what we called “environment ” based on the idea of cluster. The mathematical expression for each set of vectors is as follows: = (, (0), (1), (2), (3), ()ithnthwhereis the environment(vector) related tocounty in theyear,is thegrowth r