两类随机生态传染病动力学模型的研究

发布时间：2018-07-05 05:51

本文选题：随机干扰 + 长时间行为　；参考：《山东科技大学》2017年硕士论文

【摘要】：本文主要研究了两类生态传染病模型的动力学行为.首先研究了一类食饵染病的随机捕食者-染病食饵系统,借助随机微分方程相关理论方法,研究了随机系统正解的长时间行为,然后运用进化动力学相关理论方法研究了环境噪声作用下种群的适应性进化行为,得到了变异种群产生进化分支和进化稳定的条件,并使用数值仿真对所得理论结果进行了验证.其次研究了一类具有Beddington-DeAngelis功能反应的随机生态传染病模型,运用随机微分方程相关理论方法和一些重要的不等式,研究了系统解的长时间行为,得到了系统平均持久和灭绝的条件,并使用Matlab数值仿真对理论结果进行了验证.我们的理论结果为物种多样性的保护等工作提供了理论依据.第一章首先引入了课题的研究背景,然后介绍了随机微分方程以及进化动力学等基础理论知识.第二章首先提出了一类带有环境噪声扰动的捕食者-染病食饵模型,通过使用李雅普诺夫方法和随机微分方程相关理论,得到了模型解的长时间行为和遍历性.然后,通过适应性进化动力学方法,我们得到了一个随机干扰作用下的适合度函数,并研究了染病食饵种群中病原菌的进化分支和进化稳定性.最后,通过数值模拟对所得理论结果进行了验证.理论结果的生物意义表明大的随机干扰将会使病毒向着毒性减小的方向进化,这为疾病的控制提供了一定的理论依据.第三章首先提出了一类带有Beddington-DeAngelis功能反应的随机生态传染病模型,通过使用李雅普诺夫方法和随机微分方程相关理论,得到了模型解的长时间行为和遍历性.然后,使用随机微分方程相关理论和不等式方法,我们得到了系统平均持久性和灭绝性的条件.然后,通过数值模拟对所得结论进行了检验,结果表明物种对随机干扰的影响具有一定的抵抗能力,当随机干扰较小时,它并不会导致物种的灭绝,但是如果随机干扰足够大,它就会导致物种的灭亡.第四章对全文进行了总结,并对今后的研究工作做了前瞻性的设想.
[Abstract]:The dynamic behavior of two ecological infectious disease models was studied in this paper. In this paper, we first study a class of stochastic predator-infected predator-prey systems infected by prey. By means of the correlation theory of stochastic differential equations, we study the long-time behavior of positive solutions of stochastic systems. Then, the adaptive evolutionary behavior of the population under ambient noise is studied by using the evolutionary dynamics theory, and the conditions for the evolution branch and stability of the variation population are obtained. The theoretical results are verified by numerical simulation. Secondly, a stochastic ecological infectious disease model with Beddington-DeAngelis functional response is studied. The long-time behavior of the system solution is studied by using the stochastic differential equation theory and some important inequalities. The conditions of mean persistence and extinction of the system are obtained, and the theoretical results are verified by Matlab numerical simulation. Our theoretical results provide a theoretical basis for the conservation of species diversity. The first chapter introduces the background of the research, and then introduces the stochastic differential equations and evolutionary dynamics. In the second chapter, a predator-infected prey model with ambient noise disturbance is proposed. By using Lyapunov method and stochastic differential equation theory, the long-time behavior and ergodicity of the solution are obtained. Then, by means of adaptive evolutionary dynamics, we obtain a fitness function under random interference, and study the evolutionary branching and evolutionary stability of pathogenic bacteria in diseased bait populations. Finally, the theoretical results are verified by numerical simulation. The biological significance of the theoretical results indicates that large random interference will make the virus evolve towards the direction of decreasing toxicity, which provides a theoretical basis for disease control. In chapter 3, a stochastic ecological infectious disease model with Beddington-DeAngelis functional response is proposed. By using Lyapunov method and stochastic differential equation theory, the long-time behavior and ergodicity of the solution are obtained. Then, by using the theory of stochastic differential equation and the method of inequality, we obtain the condition of the mean persistence and extinction of the system. Then, the conclusion is tested by numerical simulation. The results show that the species has a certain resistance to the random disturbance. When the random disturbance is small, it will not lead to the extinction of the species, but if the random interference is large enough, It will lead to the extinction of the species. The fourth chapter summarizes the full text, and the future research work to make a forward-looking idea.
【学位授予单位】：山东科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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