GA算法在SIR模型参数估计中的应用

发布时间：2018-03-18 13:41

本文选题：SIR模型　切入点：生灭过程　出处：《山东大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文主要介绍了生物数学中一个经典的舱室传染病模型亦即SIR模型,目标是确定当给定原始传染数据时利用GA算法实现参数的优化反演,从而得到参数传染系数、恢复系数及基本再生率与基本再生数,进而对传染病本身的流行趋势和防治措施给出相应的参考价值。文章首先介绍了传染病动力学模型的历史发展及研究意义,综述了动力学在传染病预防控制上的优势与必要性。文章第二部分给出了基本的概念定义和理论铺垫,以随机过程-马氏过程-生灭过程为概念递进,有序给出了各自的定义及其继承式发展,以带移入的生灭过程为出发点进入下一部分的讨论;后续讨论了BDI(λ,μ,v)过程的统计推断,以对BDI过程的模拟、参数向量的估计及其数值解求解为线展开。对BDI过程的模拟采用了经典的Gillespie'sAlgithm算法;参数向量的估计是建立在推导出的似然函数上,并且在求解过程中未得到λ,v的显式解;然后给出了三种意义下可行的参数估计方法,包括遗传算法的应用。文章第三部分主要以遗传算法实现传染病动力学模型SIR模型参数反演为主。首先给出了经典的传染病动力学模型SIR模型的概念及微分方程;接下来对固定参数下的SIR过程实现路径模拟,分别给出了ODE路径下的模拟和BDI路径下的模拟;本部分的重点是对于遗传算法的介绍及其在在参数反演中的应用,给出了遗传算法的概念,详细分析了遗传算法中涉及到的一个函数三个算子的实施细节,其中一个函数指的是算法中适应度函数的确定,三个算子指的是选择算子、交叉算子、变异算子,是算法运行中必须给出的三个关键运行主体,是种群进化的潜在操盘手。文末以某寄宿制学校爆发的大范围的流感为SIR模型主体,其基本符合该模型的假设,对该流感的传染系数、恢复系数、基本再生率给出了G 算法下的参数反演结果,与参考文献中采取其他方法得到的参数估值相近,肯定了GA算法在该模型行参数中估计中的适用性和稳定性。
[Abstract]:In this paper, a classical cabin infectious disease model in biological mathematics, known as SIR model, is introduced. The purpose of this model is to determine the optimal inversion of parameters by GA algorithm when given original infectious data, so as to obtain the parameter contagion coefficient. The recovery coefficient, the basic regeneration rate and the number of basic regeneration are given, and the corresponding reference value is given for the epidemic trend of the infectious disease itself and the prevention and control measures. Firstly, the paper introduces the historical development and research significance of the dynamic model of infectious disease. This paper summarizes the advantages and necessity of dynamics in the prevention and control of infectious diseases. In the second part of the paper, the basic conceptual definition and theoretical foundation are given. The concept of stochastic process-Markov process-birth and death process is taken as the concept of progression. In this paper, the definitions and their inherited development are given in order, the birth and death process with migration is taken as the starting point to enter the next part of the discussion, and the statistical inference of the BDI (位, 渭 v) process is discussed in order to simulate the BDI process. The estimation of parameter vector and its numerical solution are linear expansion. The classical Gillespie'sAlgithm algorithm is used in the simulation of BDI process, the estimation of parameter vector is based on the derived likelihood function, and the explicit solution of 位 v is not obtained in the process of solution. Then three feasible parameter estimation methods are given. In the third part, the parameter inversion of SIR model of infectious disease dynamics model based on genetic algorithm is introduced. Firstly, the concept and differential equation of classical SIR model of infectious disease dynamics model are given. Then the path simulation of SIR process under fixed parameters is given, and the simulation of ODE path and BDI path is given respectively. The emphasis of this part is the introduction of genetic algorithm and its application in parameter inversion. The concept of genetic algorithm is given, and the implementation details of three operators of a function involved in genetic algorithm are analyzed in detail. One function refers to the determination of fitness function in the algorithm, and the three operators refer to the selection operator, the crossover operator. Mutation operator is the three key operators that must be given in the operation of the algorithm, and is the potential operator of population evolution. In the end of this paper, a large scale influenza outbreak in a boarding school is taken as the main body of the SIR model, which basically accords with the assumption of the model. The parameter inversion results under G algorithm are given for the infection coefficient, recovery coefficient and basic regeneration rate of the influenza, which are similar to the parameter estimates obtained by other methods in the reference. The applicability and stability of GA algorithm in the estimation of line parameters of the model are confirmed.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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