目前对传染病模型的研究主要限于正常系统，且大多仅对传染病模型的阈值进行分析、研究其平衡点的稳定性，对传染病模型施加控制的问题却少有研究。既往的传染病控制模型不但种类少，且缺乏综合控制。由于有些传染病模型是由微分方程和代数方程混合而形成的系统，即为广义系统，本文将应用广义系统控制理论以及概率论、最优控制理论、 Liapunov辅助理论和Zubov's方法研究对传染病模型的控制问题，并且注重对传染病模型实施综合控制。分别对某些传染病模型系统进行了精确线性化和极点配置一步设计的控制、状态反馈控制、最优控制的研究；对乙型肝炎数学模型施加免疫控制和提出降低再生数R₀、控制该传染病的措施；对某些传染病模型进行阈值分析，并探讨控制传染病的方法。主要工作有以下几个方面： 1.以往对于非线性系统的极点配置采用的是两步设计法，即精确线性化和极点配置两步法。本文将非线性广义系统的正则化理论与一步设计理论结合起来，探讨非线性广义系统的正则化、精确线性化和极点配置一步设计，并应用于Logistic增长的SIS模型，为有效控制传染病提供了理论方法。 2.本文将探讨采用两种方法建构等价于原输出函数的综合输出函数，任意配置非线性广义系统的状态空间实现的零点，使该状态空间实现系统为最小相位的方法。所构建的输出函数能直接用于建构状态反馈控制器，实施状态反馈控制。将所得结论应用于Logistic增长的SIR传染病模型，为消除该传染病提供了新方法。 3.本文将采用一种新颖的最优选择非线性系统控制器参数的方法，构造含有调节参数的性能指标，由Zubov's方法和最优化理论求出最优调节参数，实现对非线性广义系统的最优状态反馈控制和一步最优设计。将所得结论应用于Logistic增长的SIS模型，为有效、优效地控制传染病蔓延提供了理论方法。 4.根据我国乙型肝炎的流行状况，针对乙型肝炎病毒的传播方式以及各种状态间的转化模式建立了乙型肝炎数学模型，并研究了免疫控制；利用马尔可夫链的方法计算该模型中的再生数R₀，提出通过采取降低R₀的方法对乙型肝炎数学模型施加有效控制的策略。 5.分别对SIR、SIS传染病数学模型进行阈值分析，并探讨通过降低传染力，控制该传染病蔓延的理论方法。 关键词 一步设计 正则化 零点配置 状态反馈 最优控制 免疫控制隔离控制 再生数R₀

 Currently study of the epidemic models is chiefly confined to the ordinary system, and most of them are concerned with the threshold of epidemic models and the stability of the equilibrium point, which means there are few articles about control of the epidemic models. The formly models not only have few kinds but also are short of synthesize control. Due to some epidemic models are formed of couple differential and algebraic equations, namely singular system, in this thesis conducted is a study of control problem for some epidemic models by using singular system theorem, optimal control theorem probability theorem ,Zubov's method and Liapunov's auxiliary theorem, specially pay attention to synthesize control. single-step design of the feedback linearization and the pole placement, state feedback control and optimal control are studied;through exerting immunity control on mathematical model of hepatitis B, put forward a measure of reducing reproductive number R₀ for controlling the epidemic model; meanwhile, discussed are threshold and control method of some epidemic models. The main contributions are as follows: 1.Up to now, pole placement of nonlinear system is two steps which is real linearization and pole placement. In this thesis, combining normalizability of nonlinear singular control system theorem with single-step design, by that, the normalizeability, feedback linearization and the pole placement in a single step for nonlinear singular system is studied. Then, the proposed approach is finally illustrated in a Logistic grow SIS model.a new method of control the disease is theoretically presented. 2.Arbitrarily assign the zero dynamics of the state-space realization of the nonlinear singular system, made the state-space realization minimum-phase is studied. Construct the synthetic output maps which are statically equivalent to the original output maps by two ways. The calculated outputs are used to construct a state feedback controlled, and realized the state feedback control on the nonlinear singular system. The proposed method is applied to SIR epidemic model with Logistic growth control problem. By way of this, a means for control the disease is built. 3.Single-step optimal design of feedback linearization with the pole placement, optimal state feedback control for nonlinear Singular System by a new optimal selection of controller parameters for nonlinear system are studied. Construct a performance index with the parameters adjusted,which are solved by Zubov's method and standard optimization techniques. The proposed method is applied to SIS epidemic model with Logistic growth, which theoretically provides a method for control the disease effectively and optimally. 4.Mathematical model of hepatitis B is established, based on the way of its transmission and transformation. It is also studied how to effectively control these models with immunity. By way of Markov Chain to calculate the basic reproductive number R₀, the method of effectively controlling and reducing reproductive number R₀ to control the disease is also discussed. 5.Threshold of SIS and SIR epidemic models is analyzed. It is also theoretically discussed what is the effective method to control the disease by reducing the infection rate. Keywords single-step design; normalizability; assignment of zero dynamics; state feedback control; optimal control; immunity control; isolate control; reproductive number R₀