数学硕士论文代写《关于具非线性接触率传染病模型的分析与研究》（本站可提供原文购买，200元/篇）
目录
摘要5-7
ABSTRACT7-8
目录9-12
第一章绪论12-22
1.1研究背景及发展状况12-17
1.1.1不考虑出生与自然死亡等种群动力学因素15-16
1.1.2添加种群动力学因素16-17
1.2本文的主要工作17-18
1.3预备知识18-22
第二章具常数输入和非线性接触率的SIRS传染病模型22-38
2.1模型建立22-28
2.1.1解的性态与平衡点的存在性23-24
2.1.2平衡点的稳定性24-26
2.1.3数值例子26-28
2.2常数控制下解的性态28-31
2.3线性状态控制下解的性态31-34
2.4系统仿真34-37
2.4.1常数控制34-35
2.4.2线性状态反馈控制35-37
2.5本章小结37-38
第三章具密度制约和非线性接触率的SIRS传染病模型38-46
3.1模型建立38
3.2解的性态38-40
3.3平衡点的存在性40
3.4平衡点的稳定性40-43
3.5数值仿真43-45
3.6本章小结45-46
第四章具非线性接触率和易感者具Smith增长的SIRS传染病模型46-52
4.1模型建立46-47
4.2系统平衡点的存在性47-49
4.3系统平衡位置稳定性49-51
4.4本章小结51-52
第五章具非线性接触率的SIS传染病模型和SIQS传染病模型52-60
5.1模型建立52-53
5.2SIS模型分析53-54
5.3SIQS模型分析54-57
5.4数值仿真57-59
5.5本章小结59-60
第六章具指数出生和预防接种的SIRS传染病模型60-71
6.1具指数出生和连续预防接种的SIRS传染病模型61-64
6.1.1模型建立61
6.1.2平衡点的存在性61-62
6.1.3平衡点的稳定性62-64
6.2具指数出生和脉冲预防接种的SIRS传染病模型64-70
6.2.1模型建立64-65
6.2.2无病周期解的存在性65-66
6.2.3无病周期解的稳定性66-70
6.3连续接种和脉冲接种的比较70-71
第七章结束语71-72
参考文献72-77
致谢77
【摘要】 传染病的存在历来就是一种非常普遍的现象,利用动力学的方法建立传染病的数学模型,并通过数学模型对传染病进行定性与定量的分析和研究已取得了一些成果,主要集中在判定、预测疾病的发展趋势上。与以往的具有非线性接触率的传染病模型相比,本文引入了种群动力学因素,因此这类模型更精确的描述传染病传播的规律。本文讨论了模型的正不变集,运用微分方程稳定性理论分析了模型平衡点的存在性及稳定性,得出了无病平衡点和地方病平衡点全局稳定的充分条件。通过隔离染病者和对易感者进行预防接种的方式对所研究的模型施加控制,达到控制传染病的目的。主要内容如下：第一章介绍了本文所研究问题的产生背景、发展现状、所做的工作及预备知识。第二章研究了具有常数输入和非线性传染率的SIRS传染病模型。在免疫丧失的情况下,分别对模型施加常数控制、线性状态反馈控制,得到了当控制参数满足一定的条件时,地方病可以被消除的结论,并得到了平衡点全局渐近稳定的条件,仿真验证了结果的正确性。第三章研究了具有密度制约和非线性接触率的SIRS传染病模型的解的性态,分析了平衡点的存在性及正平衡点的局部稳定性问题,仿真验证了定理的正确性。第四章研究了具有非线性接触率和易感者中具有Smth增长的SIRS传染病模型,分析了该模型的正不变集和平衡位置的存在性以及各类平衡位置的稳定性问题。第五章研究了具有非线性接触率的SIS传染病模型和SIQS传染病模型,分别得到了两个模型的基本再生数,讨论了当基本再生数满足一定条件时两模型平衡点的稳定性问题,并对结果进行了仿真。第六章讨论了具有连续预防接种和脉冲预防接种的双线性发生率SIRS传染病模型,分别给出了SIRS传染病模型基本再生数。利用Lyapunov函数方法和LaSalle不变原理证明了连续预防接种下无病平衡点和正平衡点的全局稳定性；利用脉冲微分方程的Floquet乘子理论,比较定理和非线性分析的方法,系统研究了脉冲预防接种下该模型的动力学性质。给出了无病周期解全局稳定的充分条件,并对两种预防接种形式进行了比较。
数学硕士论文代写-【Abstract】 The presence of epidemic has always been a very common phenomenon and some results have been achieved by establishing epidemical models, analyzing these models qualitatively and quantitatively and predicting the trends of the epidemic. Compared with the former epidemic models with nonlinear incidence rate, this paper introduces the population dynamics factors and described the transmitting laws accurately. We discuss the positive invariant set, the existence and the stability of the equilibrium by using the stability theory of ordinary differential equation and obtain the sufficient conditions of the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium. We can attain aim to control the diffusion of epidemic by the means of isolating infected individuals and vaccinating susceptible. The main contents are as follows:Chapter one introduces the original background of the problem studied, development status, the research work and prior knowledge in the paper.Chapter two introduces the SIRS epidemic model with constant input and nonlinear transmission rate. In immunodeficiency conditions, constant control and linear state-feedback control are imposed on the model when the control parameters meet certain conditions, endemic can be eliminated and conditions of global asymptotic stability of the equilibrium. Simulation verifies the correctness of the results.Chapter three introduces the properties of solution of SIRS with density restriction and nonlinear incidence rate, the existence of equilibriums and the local stability of the positive equilibriums of the model. Simulation verifies the correctness of the results.Chapter four introduces the SIRS epidemic model with a nonlinear incidence rate and Smith Growth in susceptible populations, the positive invariant set, the equilibriums and the stability of the equilibriums of the model.Chapter five introduces the SIS epidemic model and the SIQS epidemic model with a nonlinear incidence rate. Basic reproduction numbers of two models are obtained, and stabilities of two models are discussed separately when basic reproduction numbers satisfy certain conditions. Simulation verifies the correctness of the results.Chapter six introduces the bilinear incidence SIRS epidemic models with continuous vaccination and pulse vaccination. The basic reproduction numbers of two SIRS epidemic models are given respectively. The global stability of the infection free equilibrium and positive equilibrium with continuous vaccination are proven by using Lyapunov function and LaSalle invariability principle; dynamic properties in this model with pulse vaccination are studied by using Floquet multipler theory, comparison theorem and nonlinear analysis method of the impulsive differential equation. Sufficient condition of global stability of the disease-free periodic solution is obtained and the strategies of two vaccinations are compared in the end.
【关键词】 传染病模型； 非线性接触率； 隔离率； 基本再生数； 连续接种，脉冲接种； 无病周期解； 平衡点； 全局稳定性；
【Key words】 Epidemic model； Nonlinear incidence rate； Quarantine rate； Basic reproduction number； Continuous vaccination； Pulse vaccination； Periodic infection free solution； Global stability；