文档介绍：传染病模型论文:几类传染病模型的动力学研究
【中文摘要】传染病动力学模型是生物数学模型的重要组成部分,近年来受到国内外许多学者的广泛关注与研究,并取得了很多成果。本文利用仓室建模的方法建立了几类传染病模型并研究了它们的动力学行为。首先,为了研究方便,我们给出了传染病模型的一些基本概念和研究的理论基础。其次,我们建立了具有非线性传染率的SIRS模型,给出其基本再生数,分析了其平衡点的存在性和稳定性条件,并给出其数值仿真;在此基础上我们对系统的传染率推广,并考虑连续接种疫苗,用类似方法分析其平衡点的存在性和稳定性,最后对两种模型进行对比,分析防制此类传染病的措施。第三部分,我们建立了一类具有常数输入和指数死亡且具有双线性传染率的SIRS与SIS组合的传染病模型,在给出基本再生数的基础上,分析了系统无病平衡点和地方病平衡点的存在性和稳定性,给出几种不同参数的模型仿真与对比,最后分析了如何采取应对措施防制传染病的流行。第四部分,我们简单的讨论了一下离散型SIRS传染病模型的动力学行为,利用差分方程的基本理论分析其平衡点的存在性和稳定性,给出疾病消亡或流行的条件。最后,我们对本文的工作进行总结,分析本文的特点与不足,并给出了今后研究的口标。
【英文摘要】Epidemie dynamical models are inportant parts of mathematieal models in biology. Recently, they have got much attention and been studied by lots of scholars. We have got many great results in this field. In this paper, we construct sever
al epidemic dynamical models by the method partment modeling and research their dynamical , for convenience, we introduce the background, basic concepts and some theories in epidemic models , we construct SIRS models with nonlinear incidence rate, define the reproduction number, and analyze the existence and stability of the disease-free equilibrium and the endemic equilibrium. And then we show them numerically; based on the model, we replace the nonlinear incidence rate with a general form, and consider continuous ination on S class. Then we analyze the model in a similar way. At last, pare