轮状病毒与肿瘤疾病的建模及分析

发布时间：2018-03-21 18:00

本文选题：轮状病毒　切入点：肿瘤　出处：《哈尔滨工业大学》2016年博士论文　论文类型：学位论文

【摘要】：传染病模型可以用来描述某些疾病在人与动物之间的传播,预测疾病传播的强度以及提出有效的控制措施。随着新型病原体的出现,一些学者利用许多新的数学模型来解释这些病原体对人们的影响。本文主要对轮状病毒进行建模研究,主要内容包括:首先,建立了一个考虑接种疫苗因素的轮状病毒模型,给出了基本再生数Rv的表达式,利用Lyapunov函数方法证明了当Rv1时边界平衡点全局渐近稳定,当Rv1时内部平衡点全局渐近稳定,通过模型与真实数据的拟合发现接种疫苗是控制轮状病毒传播的有效因素;其次,建立了一个描述轮状病毒与疟疾共同作用的模型,计算出基本再生数Rmr,阐明了由于共同传染的影响,当Rmr1时系统的边界平衡点未必全局渐近稳定,但如果对共同传染可以最大程度的控制,那么边界平衡点会全局渐近稳定,证明了在一定条件下系统会出现平衡点的后向分支。此外,本文还考虑了描述肿瘤增长的Kirschner-Panetta模型,通过对内部平衡点的分析得到了一个用来描述肿瘤扩散速度的参数Rs,发现在一定参数条件下系统会出现后向分支,进一步通过不确定性和敏感性分析研究了系统参数对Rs的影响,结果表明效应细胞的数量及其死亡率对肿瘤扩散有重要影响。
[Abstract]:Infectious disease models can be used to describe the spread of certain diseases between humans and animals, predict the intensity of disease transmission, and propose effective control measures. Some scholars use many new mathematical models to explain the effects of these pathogens on human beings. In this paper, rotavirus is modeled and studied. The main contents are as follows: firstly, a rotavirus model considering vaccination factors is established. The expression of the basic reproducing number Rv is given. The global asymptotic stability of the boundary equilibrium point is proved by using the Lyapunov function method, and the global asymptotic stability of the boundary equilibrium point is proved when Rv1 is the case, and the internal equilibrium point is globally asymptotically stable when Rv1 is used. It was found that vaccination was an effective factor in controlling rotavirus transmission by fitting the model with real data. Secondly, a model describing the interaction between rotavirus and malaria was established. The basic reproducing number Rmr is calculated, and it is shown that the boundary equilibrium point of the system may not be globally asymptotically stable when Rmr1 is affected by co-infection, but if the co-infection can be controlled to the greatest extent, the boundary equilibrium point will be globally asymptotically stable. It is proved that there is a backward bifurcation of the equilibrium point in the system under certain conditions. In addition, the Kirschner-Panetta model for describing tumor growth is also considered in this paper. Through the analysis of the internal equilibrium point, a parameter Rswhich is used to describe the diffusion velocity of the tumor is obtained, and it is found that the system will have backward branching under certain parameters. The effects of system parameters on Rs were further studied by uncertainty and sensitivity analysis. The results showed that the number and mortality of effector cells had an important effect on tumor diffusion.
【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：R73;R511

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