埃博拉疫情控制模型

A Mathematical Model for Ebola Control

摘要: 本模型旨在模拟埃博拉病毒爆发后，在相关地区现有的防护和医疗条件下，模拟埃博拉疫情传播情况，并对病毒的传播趋势进行预测，为相关决策部门提供一种询证决策依据。选取传染病SIR动力学模型。首先，我们构造的埃博拉病毒疫情的SIR-L模型是基于经典的SIR传染病模型和logistic模型，来模拟和预测埃博拉病毒的蔓延趋势，然后我们预测得出未来一周的新增病例，几内亚、利比里亚和塞拉利昂分别是88例、28例和238例。其次，通过分析我们得到的预测数据，结合各个国家人口规模和地理位置，根据重心法和灰色系统理论，选择出各国的最佳配送中心。里弗塞斯城、博城、玛木分别为利比里亚，塞拉利昂和几内亚的配送中心。我们选择疫情最严重的塞拉利昂作为生产国，博城作为生产中心。最后，基于最优配送中心和生产中心，参考现代一些先进的物流系统和现代企业物流系统运营经验，我们设计了应急物资分配三级模型。即以生产中心作为网络第一级，三个国家的配送中心作为网络第二级节点，各国中每个县的城镇中心作为第三级节点。我们以埃博拉疫情初期配送时间最短，疫情后期救援体系成本最低为原则，设计了物资分配网络体系。

Abstract: This paper aims to analyze the cases of Ebola in West Africa, forecast the future trend of the spread of the virus, and provide some consulting opinions for related departments to make decisions. Firstly, we construct the SIR-L model for Ebola epidemics based on the classical infectious diseases SIR model and the Logistic model to simulate and predict the spread trends of the virus. We get that the Ebola has crossed the peak period in the three main countries, but the cases of the Ebola are still at a high level. Then we forecast the new cases in the next week: 88, 28 and 238 cases for Guinea, Liberia, and Sierra Leone, respectively. Secondly, by analyzing the data that we forecast, combing with the population size and geographical location of each country, a dynamical model is established based on gravity center method and gray theory, which are utilized to select the optimal distribution center. It reveals that River Cess, Bo, Mamou are the optimal distribution centers of Liberia, Sierra Leone, and Guinea, respectively. Sierra Leone, the hardest-hit area, is se-lected as the production country, and Bo is selected as the production center. Finally, based on the optimal distribution center and production center, we develop the distribution model of emergency supplies in three layers, which refers to some of advanced sophisticated logistics systems and operational experiences of modern enterprise logistics systems. That is to say, the production center is considered as the first layer of the network; the distribution center of the three countries is the second layer; and the town center of each country’s county is the third layer. We design a distribution network system based on the principle that the delivery time of the Ebola is the shortest in the beginning, and the cost of the rescue system is the lowest in the later period.