两类院内感染抗生素耐药性模型的稳定性研究

发布时间：2018-01-06 09:05

本文关键词：两类院内感染抗生素耐药性模型的稳定性研究　出处：《中北大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文第一章通过分析世界卫生组织2014年以来关于抗生素耐药性方面的调查报告,以及我国细菌耐药监测网最新的细菌耐药检测报告,论证了全球抗生素耐药性的严峻形势.通过分析近几年发表的医院内抗生素耐药性传播模型的基本建模思路、论证方法、所得结论,总结出了抗生素耐药性模型研究发展的两个趋势.最后系统地介绍了抗生素耐药性的传播机理、基本概念和抗生素耐药性基本数学模型的分类框架.本文第二章建立了一类带有感染期时滞和直接传播、间接传播两种传播方式的抗生素耐药性院内传播模型.同时引入感染期时滞t和患者经过感染期后仍在院内的概率e~(-μt).然后定义疾病暴发的阈值0R,运用Routh-Hurwitz判据、Lasalle-Liapunov不变集原理,证明了当R_01时,对于任意的时滞τ≠0无病平衡点是局部且全局渐近稳定的;当R_01时,地方病平衡点存在且唯一,对于任意的时滞τ≠0,地方病平衡点是局部且全局渐近稳定的.最后进行数值模拟验证了结论的正确性,分析了感染期长短对疾病传播峰值的影响.本文第三章在第二章模型的基础上,将模型环境细化到ICU病房,建立了一类带有多种预防措施参数及治疗函数的ICU病房内抗生素耐药性单向转变传染病模型.通过定义疾病暴发的阈值R_0,运用Routh-Hurwitz判据、第二加性复合矩阵原理,证明了当R_01时,无病平衡点是局部渐近稳定的;当R_01时,地方病平衡点具有唯一存在性是局部且全局渐近稳定的.最后运用数值模拟的方法验证了结论的正确性.
[Abstract]:Since the first chapter of this paper through the analysis of the WHO in 2014 on the investigation report of antibiotic resistance, and bacterial resistance monitoring network of China's latest bacterial resistance test report, demonstrates the severe situation of global antibiotic resistance. Through the analysis of the basic modeling ideas, published in recent years in hospital antibiotic resistance propagation model demonstration method, the conclusion. Summarizes the two development trend of antibiotic resistance model. Finally, systematically introduces the propagation mechanism of antibiotic resistance, the basic concept and classification framework based on the mathematical model of antibiotic resistance. The second chapter establishes an infection delay and direct communication with the model, spread of antibiotic resistance hospital indirect spread of two modes of at the same time. The time delay and t infection of patients after infection in the hospital after the probability of e~ (- t). And then define the threshold of 0R disease outbreaks, using Routh-Hurwitz criterion, Lasalle-Liapunov invariance principle shows that when R_01, the delay is not equal to 0 for any disease free equilibrium is locally and globally asymptotically stable; when R_01, the endemic equilibrium exists and is unique, for any delay = 0, balance where the disease is local and global asymptotic stability. Finally, numerical simulation is carried out to verify the correctness of the result, analyzes the impact of infection duration of disease transmission peak. The third chapter in the second chapter based on the model, the model is refined to the ICU ward, established a variety of preventive measures and treatment function parameters the ICU ward of antibiotic resistance monotropy infectious disease model. Through the threshold R_0 definition of disease outbreaks, using Routh-Hurwitz criterion, second additive compound matrix principle, shows that when R_01, the disease free equilibrium The point is locally asymptotically stable; when R_01, the endemic equilibrium is unique and globally asymptotically stable. Finally, the correctness of the conclusion is verified by numerical simulation.

【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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