一类传染病模型的优化控制和数据模拟
发布时间：2018-11-05 10:55
【摘要】：传染病一直是威胁人类健康的重要病症之一,人们通过研究传染病的发病机理及传播规律来制定科学的控制策略是传染病控制研究的主要方法之一。然而在过去的传染病控制研究中,大多认为在流行病传播周期内其传播系数为一个确定的常数,这不能够准确描述一些持续时间长且季节性较明显的传染病(如流感、猩红热等)。本文主要针对日常生活中一般的甲乙类传染病,结合Qingxia Zhang等人的SEI_QI_NAR模型和G.Chowell等人的SEAIJRD模型,建立新的SEIJAR模型。全文主要研究了以下问题:1.考虑日常生活中一般的传染病的特性,认为其治疗药物是充足的,在此基础上建立SEIJAR模型。该模型有两点重要的特性:一是该模型考虑了人口的流动性,在模型中包括了从外部输入的潜伏者和无症状感染者;二是在模型中考虑了疫苗的使用以及隔离控制措施。患病者被发现症状后立刻接受治疗,对部分病情较为严重的病例采取隔离治疗的方案。利用庞特里亚金极大值原理,将SEIJAR模型的最优控制问题转化为最小哈密顿函数问题,证明最优控制的存在性,并给出最优控制的具体形式。2.结合许多流行病的发病率在温带地区都表现出强烈的季节性波动的情况,在SEIJAR模型的基础上,引入季节性影响因素,并认为季节性影响表现在疾病传播速度β上。通过对江苏省2013年1月至2016年7月的每月的甲乙类传染病发病数据分析,找出季节性影响下的疾病传播速度β的表现形式。利用庞特里亚金极大值原理给出带有季节性影响的SEIJAR模型的最优控制的具体形式。最后,借助Runge-Kutta迭代算法并通过数值仿真验证了最优控制的有效性,以及和季节性影响相关的几个参数的敏感度分析,说明了受季节性影响的传染病爆发后,考虑季节因素对传染病控制的最优方案的制定有很大的影响。
[Abstract]:Infectious diseases have always been one of the most important diseases threatening human health. It is one of the main methods of infectious disease control that people make scientific control strategies by studying the pathogenesis and transmission law of infectious diseases. However, in previous studies on infectious disease control, the transmission coefficient was considered to be a definite constant during the epidemic period, which could not accurately describe some infectious diseases (such as influenza) that lasted for a long time and were more seasonal. Scarlet fever, etc In this paper, a new SEIJAR model is established based on the SEI_QI_NAR model of Qingxia Zhang et al and the SEAIJRD model of G.Chowell et al., aiming at the common class A and B infectious diseases in daily life. This paper mainly studies the following questions: 1. Considering the characteristics of common infectious diseases in daily life, the SEIJAR model was established. The model has two important characteristics: one is that the model takes into account the mobility of the population, and the model includes lurks and asymptomatic infections imported from the outside; the other is that the use of vaccines and isolation control measures are taken into account in the model. Patients are treated as soon as symptoms are discovered, and some of the more serious cases are treated in isolation. In this paper, the optimal control problem of SEIJAR model is transformed into the least Hamiltonian function problem by using Ponteriagin maximum principle, the existence of optimal control is proved, and the concrete form of optimal control is given. 2. Combined with the strong seasonal fluctuation of the incidence of many epidemics in temperate regions, based on the SEIJAR model, the seasonal factors were introduced, and the seasonal effects were considered to be on the speed of disease transmission 尾. By analyzing the monthly incidence data of A and B infectious diseases in Jiangsu Province from January 2013 to July 2016, we found out the expression form of disease transmission speed 尾 under seasonal influence. The concrete form of optimal control of SEIJAR model with seasonal influence is given by using Ponteriagin maximum principle. Finally, with the help of Runge-Kutta iterative algorithm and numerical simulation, the effectiveness of optimal control and sensitivity analysis of several parameters related to seasonal effects are verified. The consideration of seasonal factors has a great influence on the formulation of optimal scheme for infectious disease control.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O232;R181
[Abstract]:Infectious diseases have always been one of the most important diseases threatening human health. It is one of the main methods of infectious disease control that people make scientific control strategies by studying the pathogenesis and transmission law of infectious diseases. However, in previous studies on infectious disease control, the transmission coefficient was considered to be a definite constant during the epidemic period, which could not accurately describe some infectious diseases (such as influenza) that lasted for a long time and were more seasonal. Scarlet fever, etc In this paper, a new SEIJAR model is established based on the SEI_QI_NAR model of Qingxia Zhang et al and the SEAIJRD model of G.Chowell et al., aiming at the common class A and B infectious diseases in daily life. This paper mainly studies the following questions: 1. Considering the characteristics of common infectious diseases in daily life, the SEIJAR model was established. The model has two important characteristics: one is that the model takes into account the mobility of the population, and the model includes lurks and asymptomatic infections imported from the outside; the other is that the use of vaccines and isolation control measures are taken into account in the model. Patients are treated as soon as symptoms are discovered, and some of the more serious cases are treated in isolation. In this paper, the optimal control problem of SEIJAR model is transformed into the least Hamiltonian function problem by using Ponteriagin maximum principle, the existence of optimal control is proved, and the concrete form of optimal control is given. 2. Combined with the strong seasonal fluctuation of the incidence of many epidemics in temperate regions, based on the SEIJAR model, the seasonal factors were introduced, and the seasonal effects were considered to be on the speed of disease transmission 尾. By analyzing the monthly incidence data of A and B infectious diseases in Jiangsu Province from January 2013 to July 2016, we found out the expression form of disease transmission speed 尾 under seasonal influence. The concrete form of optimal control of SEIJAR model with seasonal influence is given by using Ponteriagin maximum principle. Finally, with the help of Runge-Kutta iterative algorithm and numerical simulation, the effectiveness of optimal control and sensitivity analysis of several parameters related to seasonal effects are verified. The consideration of seasonal factors has a great influence on the formulation of optimal scheme for infectious disease control.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O232;R181
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