近年来国内外学者普遍关注到具有迁移率的多斑块模型。本文依据仓室建模的基本思想并考虑隔离患者和预防接种等因素建立了几类具有种群迁移的SEIQR传染病模型。通过定性分析和数值模拟研究了模型的动力学性态，深入地探讨了各因素对疾病发展的影响。主要内容如下： 首先，在两斑块SEIQR传染病模型中考虑了易感者具有迁移率，针对该模型采用再生矩阵的方法得到疾病的基本再生数 。综合运用Lyapunov稳定性理论、分歧理论等，讨论了无病平衡点、边界平衡点、地方病平衡点的存在性、稳定性以及Hopf分歧的存在性。 其次，假设易感者和潜伏者或者易感者和感染者具有迁移率且两个斑块中模型的参数相同，应用再生矩阵的方法得到疾病的基本再生数 ，采用Lyapunov稳定性理论，分别讨论了无病平衡点和地方病平衡点的存在性，以及其全局渐近稳定性。并进行了数值模拟，结果表明当 时，两个斑块中感染者均收敛于地方病平衡点，即疾病将会在两个斑块中流行形成地方病。 然后，假设易感者、潜伏者以及感染者均具有迁移率，针对该模型采用再生矩阵的方法得到疾病的基本再生数 并讨论了无病平衡点的存在惟一性以及其全局渐近稳定性。采用2003年卫生部公布的北京市与山西省的SARS传播数据进行数值模拟，发现模型的预测值与临床数据能够较好的吻合。 最后，建立了一类具有n个斑块SEIQR模型，计算了疾病的基本再生数 ，研究了无病平衡点的存在性以及稳定性。

Recently, the multiple patches model with migration has been widely concerned by experts and scholars at home and abroad. According to the basic idea of compartment modeling and taking into account of the factors, such as isolation of patients, vaccination et al., several kinds of SEIQR epidemic models with population migration are established. The dynamics of the models are investigated by qualitative and numerical analysis and the influence of various factors on the development of the disease is explored. The contents of this paper are mainly arranged as follows. First, assuming that only the susceptible individuals travel between the two patches, an SEIQR epidemic model is formulated. The basic reproduction number R0 is computed by the method of the next generation matrix. Besides, the existence and global stability of the disease free equilibrium, the boundary equilibrium and the endemic equilibrium are mainly discussed based on the theory of the Lyapunov stability theory, and the existence of the Hopf bifurcation is researched by the bifurcation theory. Second, assuming that the susceptible and the latent individuals or the susceptible and the infected individuals can travel between the two patches and the parameters in the two patches model are the same, the basic reproduction number R0 of the disease is defined and the existence and global stability of the disease free equilibrium and endemic equilibrium are proved by the theory of Lyapunov stability. Numerical simulations indicate that all the trajectories of the model converge to the endemic equilibrium if R0>1. Then, assuming that the susceptible, the latent and the infected individuals can travel between the two patches, the basic reproduction number R0 is calculated by the next generation matrix method, and the existence and global stability of the disease free equilibrium and endemic equilibrium are studied. Numerical results indicate that predicted values of the model coincide with the clinical SARS data of Beijing and Shanxi province released by the ministry of health in 2003. Finally, The model of SEIQR is extended to n patches one and the basic reproduction number can be studied, and the existence and stability of the disease-free equilibrium are investigated.