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目的研究埃博拉出血热的病情发展规律,提出可行的药物配送系统方案。方法根据2015年美国大学生数学建模竞赛A题的题目—消除埃博拉,建立SIR流行病模型预测该疾病的发展。根据2015年2月6日WHO的非洲各地区患病情况的数据,在疫区地图上选取了36个有感染者的地区并将其坐标位置标记出来,通过基于模拟退火的TSP(Traveling Sales Man Problem)算法研究药物配送系统。通过分析来自2015年2月6日WHO的非洲各地区患病情况的数据,建立以上两个模型在Matlab 7.0中运行,从而寻找一条花费最少运输路径最短的最优路径。结果 SIR传染病模型可以表示感染者的数目随着时间的关系,显示感染者与易感人群之间的数量变化关系;还可以分别预测感染者与易感者的数量变化趋势。根据基于模拟退火算法的TSP模型,在药物配送系统中可以找到一条花费最少、运输路径最短的最优路径,最优路径的最短距离为2 565.321 km,弗里敦(塞拉利昂的首都)和凯鲁阿内(位于几内亚)是物流分配中心,根据药物配送系统的制定规则,其他的地区将分别从这两个城市开始一个接一个有序地收到药品。结论隔离是阻止埃博拉病毒传播最有效的措施。只有将病人隔离和最短的药物运送路径结合起来才能有效地预防埃博拉疫情。
Objective To study the development of Ebola hemorrhagic fever and to propose a feasible drug delivery system. Methods Based on the title A of the 2015 American College Students Mathematical Contest in Modeling - Ebola elimination, the SIR epidemic model was established to predict the development of the disease. According to the WHO data on the prevalence of various regions of Africa on February 6, 2015, 36 infected areas were selected on the map of the affected area and their coordinates were marked. Traveling Sales Man (TSP) based simulated annealing Problem Algorithm for Drug Delivery System. By analyzing data from the February 6, 2015 WHO prevalence in various regions of Africa, the above two models were built to run in Matlab 7.0 to find the optimal path with the shortest transport path. Results The SIR epidemic model can show the relationship between the number of infected persons and the susceptible population as a function of time, and can also predict the change trend of the number of infected and susceptible individuals respectively. According to the TSP model based on the simulated annealing algorithm, an optimal path with the least cost and the shortest transport path can be found in the drug delivery system. The shortest distance of the optimal path is 2,565.321 km, Freetown (the capital of Sierra Leone) Arne (Guinea) is the logistics distribution center, and according to the rules governing the drug delivery system, other regions will receive medicines one after another in order from the two cities. Conclusion Isolation is the most effective measure to prevent the spread of Ebola virus. Ebola outbreaks can be effectively prevented only by combining patient isolation with the shortest drug delivery route.