几类具有状态依赖脉冲控制的传染病模型研究
发布时间：2019-04-10 17:33
【摘要】：近年来,脉冲微分方程的研究热点正逐步由固定时刻脉冲控制系统转向状态依赖脉冲控制系统.在此背景下,本文详细讨论了状态依赖脉冲控制对具有种群总数变化传染病模型动力学的影响,主要研究内容如下:1.第一部分(对应第2节),主要讨论了两类具有人口总数变化,连续接种和状态依赖脉冲接种SIS传染病模型的动力学.在第一个控制模型中,我们以染病者在人口总数中所占的比例作为检测阈值,通过Poincare映射,类Poincare准则和定性分析方法,得到了该控制模型正的阶-1周期解的存在性和轨道渐近稳定性.其次,将易感者在人口总数中所占的比例作为检测阈值,提出了第二个控制模型,建立了该控制模型无病周期解存在和全局轨道渐近稳定性的判别准则.最后,通过数值模拟验证了主要的理论结果和状态依赖脉冲控制措施的可行性.2.第二部分(对应第3节),为了探索布鲁士菌病在反刍动物之间的传播动力学,建立了两类具有状态依赖脉冲控制和种群总数变化的SIRS传播模型.讨论状态依赖脉冲控制策略对疾病消除和控制的影响.首先,以染病者在种群中所占比例作为检测阈值提出具有医疗资源有限的状态依赖脉冲接种的SIRS传染病模型.通过定性分析,比较原理等方法,得到了该控制模型正的阶-1或阶-2周期解存在和轨道渐近稳定的充分条件.进一步,将易感者在种群中所占的比例作为检测阈值建立了另一个具有状态依赖脉冲控制策略的SIRS传染病模型,讨论了该控制模型正的阶-1周期解和无病周期解的存在性和轨道渐近稳定性.数值模拟验证了理论结果的正确性和状态依赖脉冲控制策略的可行性.3.第三部分(对应第4节),考虑到当前有限的医疗资源,本节提出了一类具有状态依赖脉冲控制和因病死亡的SIR传染病模型,通过Poincare映射,类Poincare准则和定性分析的方法,建立了该模型正的阶-1或阶-2周期解存在和轨道渐近稳定的判别准则.最后,通过数值模拟验证了理论结果的正确性.
[Abstract]:In recent years, the research focus of impulsive differential equations is gradually changing from fixed-time impulsive control system to state-dependent impulsive control system. Under this background, the effects of state-dependent impulse control on the dynamics of infectious disease models with population change are discussed in detail. The main contents are as follows: 1. In the first part (corresponding to Section 2), the dynamics of two kinds of SIS epidemic models with population change, continuous inoculation and state-dependent pulse vaccination are discussed. In the first control model, we use the proportion of the infected person in the total population as the detection threshold, and use Poincare mapping, Poincare-like criterion and qualitative analysis method. The existence of positive order-1 periodic solution and the asymptotic stability of orbit for the control model are obtained. Secondly, taking the proportion of susceptible persons in the total population as the detection threshold, a second control model is proposed, and the criteria for the existence of disease-free periodic solutions and the asymptotic stability of the global orbit are established. Finally, the main theoretical results and feasibility of state-dependent pulse control are verified by numerical simulation. 2. In the second part (corresponding to Section 3), in order to explore the transmission dynamics of brucellosis among ruminants, two kinds of SIRS propagation models with state-dependent pulse control and population total variation were established. The effects of state-dependent pulse control strategy on disease elimination and control were discussed. Firstly, a SIRS epidemic model with limited medical resources and state-dependent pulse vaccination was proposed based on the proportion of infected persons in the population as the detection threshold. By means of qualitative analysis and comparison principle, the sufficient conditions for the existence of positive order-1 or order-2 periodic solutions and the asymptotic stability of the orbit of the control model are obtained. Furthermore, another SIRS epidemic model with state-dependent impulse control strategy is established by using the proportion of susceptible persons in the population as the detection threshold. The existence and orbit asymptotic stability of positive order-1 periodic solutions and disease-free periodic solutions for the control model are discussed. Numerical simulation verifies the correctness of the theoretical results and the feasibility of the state-dependent pulse control strategy. 3. In the third part (corresponding to Section 4), considering the current limited medical resources, this section proposes a kind of SIR epidemic model with state-dependent pulse control and disease-related death. It adopts Poincare mapping, Poincare-like criterion and qualitative analysis method. The criteria for the existence of positive order-1 or order-2 periodic solutions and the asymptotic stability of orbits for the model are established. Finally, the correctness of the theoretical results is verified by numerical simulation.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175;O231
，
本文编号：2455992
[Abstract]:In recent years, the research focus of impulsive differential equations is gradually changing from fixed-time impulsive control system to state-dependent impulsive control system. Under this background, the effects of state-dependent impulse control on the dynamics of infectious disease models with population change are discussed in detail. The main contents are as follows: 1. In the first part (corresponding to Section 2), the dynamics of two kinds of SIS epidemic models with population change, continuous inoculation and state-dependent pulse vaccination are discussed. In the first control model, we use the proportion of the infected person in the total population as the detection threshold, and use Poincare mapping, Poincare-like criterion and qualitative analysis method. The existence of positive order-1 periodic solution and the asymptotic stability of orbit for the control model are obtained. Secondly, taking the proportion of susceptible persons in the total population as the detection threshold, a second control model is proposed, and the criteria for the existence of disease-free periodic solutions and the asymptotic stability of the global orbit are established. Finally, the main theoretical results and feasibility of state-dependent pulse control are verified by numerical simulation. 2. In the second part (corresponding to Section 3), in order to explore the transmission dynamics of brucellosis among ruminants, two kinds of SIRS propagation models with state-dependent pulse control and population total variation were established. The effects of state-dependent pulse control strategy on disease elimination and control were discussed. Firstly, a SIRS epidemic model with limited medical resources and state-dependent pulse vaccination was proposed based on the proportion of infected persons in the population as the detection threshold. By means of qualitative analysis and comparison principle, the sufficient conditions for the existence of positive order-1 or order-2 periodic solutions and the asymptotic stability of the orbit of the control model are obtained. Furthermore, another SIRS epidemic model with state-dependent impulse control strategy is established by using the proportion of susceptible persons in the population as the detection threshold. The existence and orbit asymptotic stability of positive order-1 periodic solutions and disease-free periodic solutions for the control model are discussed. Numerical simulation verifies the correctness of the theoretical results and the feasibility of the state-dependent pulse control strategy. 3. In the third part (corresponding to Section 4), considering the current limited medical resources, this section proposes a kind of SIR epidemic model with state-dependent pulse control and disease-related death. It adopts Poincare mapping, Poincare-like criterion and qualitative analysis method. The criteria for the existence of positive order-1 or order-2 periodic solutions and the asymptotic stability of orbits for the model are established. Finally, the correctness of the theoretical results is verified by numerical simulation.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175;O231
，
本文编号：2455992
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