非典型性肺炎传播模型研究

发布时间：2018-06-20 15:59

本文选题：非典型性肺炎(SARS) + 微分方程模型　；参考：《大连理工大学》2005年硕士论文

【摘要】：非典型性肺炎(SARS)时疫从爆发到结束,对中国的社会、经济发展产生了巨大的影响。由于SARS流行时间短,对它的传播机理研究得还不够深入,无法找到有效的预防手段。当SARS疫情再度爆发时,如果能建立数学模型并在计算机上实时模拟、预测其疫情的发展趋势,对于控制疫情、维护社会稳定、保证经济发展是非常有意义的,对政府及有关部门科学决策也是至关重要的。本文参考了大量传染性疾病传播的文献,在前人研究的基础上,细致而又深入地研究了SARS的传播模型,并在理论研究所得到的成果的基础上,建立了SARS传播仿真实验系统。本文在理论研究方面建立了三个SARS传播模型,从不同的角度反映了SARS的传播扩散。本文首先建立了SARS传播微分方程模型,在传统的SIR模型基础上增加了自由带菌者F。自由带菌者是SARS得以传播的根源,可以控制他来控制SARS的传播。仿真结果和实际数据相吻合,证明了该模型的合理性。SARS的传染规律是一个非常复杂的问题,具有高度的非线性。神经网络是非线性复杂系统常用的建模、预测方法,本文的第二种方法就是利用了神经网络在非线性建模领域的优势,建立了基于神经网络的SARS传播模型。根据SARS的传播特点确定了神经网络结构,并用实际数据训练该网络。利用训练好的网络进行预测,预测结果和实际数据相比误差小、准确度高。本文的重点是建立了基于复杂网络的SARS传播模型。复杂网络是最近几年新兴的研究领域,依据复杂网络理论,要想模拟现实中的社会网络,构造的复杂网络必须满足有小的特征路径长度、大的簇系数和顶点度满足power-law分布。本文所建立的二维复杂网络满足了这一要求,并研究了SARS在该网络上的动态传播行为,得出了远程连接边的存在大大加快了SARS传播等一些符合实际情况的结论。用该模型模拟现实情况,仿真结果能很好的解释北京市的实际数据。本文用三种方法研究了SARS的传播行为,并开发了SARS传播仿真实验系统,对SARS再次爆发和出现类似的传染性疾病的控制工作具有现实意义。
[Abstract]:SARS (atypical pneumonia) outbreak to the end of the epidemic has had a great impact on China's social and economic development. Because of the short time of SARS epidemic, the study of its spreading mechanism is not enough, and it is impossible to find effective preventive measures. When the SARS epidemic erupts again, if we can establish a mathematical model and simulate it in real time on a computer, and predict the development trend of the epidemic situation, it is very meaningful for us to control the epidemic situation, maintain social stability, and ensure economic development. It is also very important for the government and related departments to make scientific decisions. In this paper, referring to a large number of literature on the spread of infectious diseases, on the basis of previous studies, the transmission model of SARS is studied in detail and deeply, and the simulation experimental system of SARS transmission is established on the basis of the results obtained from theoretical research. In this paper, three models of SARS transmission are established, which reflect the spread of SARS from different angles. In this paper, the differential equation model of SARS transmission is established, and the free carrier F is added based on the traditional Sir model. The free carrier is the root of SARS transmission, it can be controlled to control the spread of SARS. The simulation results are in agreement with the actual data. It is proved that the model is reasonable. The infection law of SARS is a very complicated problem and has a high degree of nonlinearity. Neural network is a common modeling and forecasting method for nonlinear complex systems. The second method in this paper is to make use of the advantages of neural networks in the field of nonlinear modeling and to establish a SARS propagation model based on neural networks. According to the transmission characteristics of SARS, the neural network structure is determined, and the network is trained with actual data. Compared with the actual data, the prediction results are less error and higher accuracy by using the trained network. The emphasis of this paper is to establish a SARS transmission model based on complex network. Complex network is a new research field in recent years. According to the theory of complex network, in order to simulate the social network in reality, the constructed complex network must satisfy the power-law distribution with small characteristic path length, large cluster coefficient and vertex degree. The two-dimensional complex network established in this paper satisfies this requirement and studies the dynamic propagation behavior of SARS on the network. It is concluded that the existence of remote connection edge greatly speeds up the spread of SARS and so on. Using this model to simulate the actual situation, the simulation results can well explain the actual data of Beijing. In this paper, three methods are used to study the transmission behavior of SARS, and a simulation experimental system of SARS transmission is developed, which is of practical significance for the control of SARS outbreak and the emergence of similar infectious diseases.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2005
【分类号】：R181.2

【共引文献】