舌状绦虫传染病模型及其稳定性分析

发布时间：2019-04-10 14:24

【摘要】：本文依据舌状绦虫疾病的传播过程,构建了两个动力学模型,并对其性态加以分析.第一章,介绍了舌状绦虫病的生物背景和传播机制,以及寄生虫感染食饵——捕食者系统的动力学模型研究进展.第二章,建立了具有双线性功能反应函数的动力学模型.首先,证明了模型解的正性和有界性,其次,计算出了模型基本再生数和讨论了模型平衡点的存在性,接着,分析了平衡点的局部稳定性.最后,分析了部分平衡点的全局稳定性.第三章,建立了具有第Ⅱ类功能性反应函数的动力学模型.首先,证明了模型解的正性和有界性.其次,给出基本再生数和讨论了平衡点的存在性.最后,分析了模型平衡点的存在性及局部稳定性.第四章,简要回顾了本文的主要工作,介绍了模型的实际意义,并对本文工作的不足之处及进一步研究方向进行了讨论.
[Abstract]:In this paper, according to the transmission process of tapeworm disease, two dynamic models were constructed and their behavior was analyzed. In the first chapter, the biological background and transmission mechanism of hyoid tapeworm and the dynamics model of prey-predator system infected by parasites are reviewed. In the second chapter, the dynamic model with bilinear functional response function is established. First, the positive and boundedness of the solution of the model is proved. Secondly, the basic regeneration number of the model is calculated and the existence of the equilibrium point is discussed. Secondly, the local stability of the equilibrium point is analyzed. Finally, the global stability of partial equilibrium point is analyzed. In the third chapter, the kinetic model with the type 鈪，

本文编号：2455872