ANALYSIS OF A CHEMOSTAT MODEL FOR BACTERIA AND VIRULENT BACTERIOPHAGE

ANALYSIS OF A CHEMOSTAT MODEL FOR BACTERIA AND VIRULENT BACTERIOPHAGE
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细菌和毒力噬菌体恒化器模型的分析

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发表时间：
2002
期刊：
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通讯作者：
Yanbin Tang
Yanbin Tang
中科院分区：
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文献类型：
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作者：
E. Beretta;F. Solimano;Yanbin Tang

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本文的目的是研究 一个细菌和噬菌体系统模型的解 恒化器一个普遍的模型是由Levin，Stewart和Chao首先提出的 [13]然后，一个具体的一个，由Lenski和莱文[12]。数值 模拟来自[12，13]中提到的实验数据。在我们 下面介绍的知识分析是第一个数学 尝试分析细菌和毒力噬菌体的模型， 提出了两个新的前沿：1）延迟（潜伏期）的建模 在线性稳定性中加入实际的死亡率 分析了带时滞依赖参数的特征方程 直到最近Beretta和Kuang [5]才提供了几何稳定性 沿着介绍了开关判据的应用; 通过三个完整延迟级的动态建模可以简化为 二是用积分表示感染者的密度 细菌所研究的模型的基本性质是： 平衡点的存在性、正不变性和解的有界性 和持久性的结果。第二，使用几何稳定开关 在具有时滞相关参数的时滞微分系统中， 通过分析系统的稳定性， 相应的系数随时间变化的特征方程 延迟（潜伏期）。数值模拟 以说明局部稳定性的结果。然后，我们研究了 基于Liapunov的边界平衡点的全局渐近稳定性 功能方法最后，对模型进行了讨论。
The purpose of this paper is to study the mathematical properties of the solutions of a model for bacteria and virulent bacteriophage system in a chemostat. A general model was first proposed by Levin, Stewart and Chao [13] and then, a specific one, by Lenski and Levin [12]. The numerical simulations come from the experimental data referred in [12,13]. In our Knowledge the analysis presented herefollowing is the first mathematical attempt to analyse the model of bacteria and virulent bacteriophage and presents two fresh frontiers: 1) the modeling of delay (latency period) incorporating the realistic through time death rate in linear stability analysis brings to characteristic equations with delay dependent parameters for which only recently Beretta and Kuang [5] provided a geometric stability switch criterion which application is presented along the paper; 2) the modelling of the dynamics through three full delay stages can be reduced to two using the integral representation for the density of infected bacteria. The basic properties of the model which are investigated are the existence of equilibria, positive invariance and boundedness of solutions and permanence results. Second, using the geometric stability switch criterion in the delay differential system with delay dependent parameters, we present the local asymptotic stability of the equilibria by analyzing the corresponding characteristic equation which coefficients depend on the time delay (the latency period). Numerical simulations are presented to illustrate the results of local stability. Then, we study the global asymptotic stability of the boundary equilibria via Liapunov functional method. Finally, we give a discussion about the model.