几类具有人工干预行为生态流行病模型及其控制研究

发布时间：2018-01-28 22:05

  本文关键词： 生态流行病 全局稳定性 平衡点 数值模拟　出处：《兰州交通大学》2015年硕士论文　论文类型：学位论文

【摘要】：流行病长期威胁着人类健康,在人类发展的历史长河中扮演着不同的角色。它不仅威胁人类生命财产安全,更是无数家禽牲畜的克星。近些年来,不少专家学者研究了几类传染病的流行规律。发现了传染病既在人群中传播,也在生物种群中传播,而且很容易造成交叉感染。为此,研究生态流行病显得尤为重要。(1)研究一类具有治愈率且捕食者染病的生态流行病模型。通过雅可比矩阵判断平衡点E0,E1的局部稳定性,构造Dulac函数判断平衡点E0的全局稳定性,得到当此时患病的捕食者灭绝,食饵和易感捕食者共存。(2)分析食饵染病的生态流行病动力学模型,讨论了平衡点E0,E2的局部稳定性。构造V函数判断平衡点E0的全局稳定性,得到当c(d2+u2)时,V≤0。即食饵种群灭绝,捕食者种群持续生存。(3)探讨一类具有垂直传染的生态流行病动力学模型。根据当R0≤1时,平衡点E0的全局稳定性以及当R01时,平衡点E*的全局稳定性,进行Matlab数值模拟,直观地观察食饵,捕食者种群数量随时间t的变化情况。
[Abstract]:Epidemic disease is a long-term threat to human health and plays a different role in the history of human development. It not only threatens the safety of human life and property, but also the enemy of countless poultry and livestock in recent years. Many experts and scholars have studied the epidemic law of several infectious diseases, and found that infectious diseases not only spread among the population, but also in the biological population, and it is easy to cause cross-infection. A class of ecological epidemic models with cure rate and predator infection are studied. The local stability of equilibrium point E _ (0) E _ (1) is judged by Jacobian matrix. The Dulac function is constructed to determine the global stability of the equilibrium point E _ 0. When the diseased predator is extinct and the prey and susceptible predator coexist. In this paper, the local stability of equilibrium point E _ 0 E _ 2 is discussed. The global stability of equilibrium point E _ 0 is determined by constructing V function, and it is obtained that V 鈮，

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