A delay reaction-diffusion model of the spread of bacteriophage infection
A delay reaction-diffusion model of the spread of bacteriophage infection
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DOI：
10.1137/s0036139903436613
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发表时间：
2005-01-01
影响因子：
1.9
通讯作者：
Kuang, Y
中科院分区：
文献类型：
--
作者：
Gourley, SA;Kuang, Y
本文是最近试图通过数学建模来了解海洋噬菌体感染动力学的延续。以前的作者提出了常微分时滞方程系统的延迟依赖系数。在本文中，我们继续这些研究在两个方面。首先，我们表明，动态是敏感的噬菌体死亡率函数，特别是我们用来衡量密度依赖性噬菌体死亡率的参数。其次，我们将空间效应推导，在一个空间维度，延迟reactiondiffusion模型中的延迟项是严格推导通过求解冯Foerster方程。使用这个模型，我们正式计算病毒感染通过域传播的速度，并研究这个速度如何依赖于系统参数。数值模拟表明，根据线性理论的最小速度是传播的渐近速度。
This paper is a continuation of recent attempts to understand, via mathematical modeling, the dynamics of marine bacteriophage infections. Previous authors have proposed systems of ordinary differential delay equations with delay dependent coefficients. In this paper we continue these studies in two respects. First, we show that the dynamics is sensitive to the phage mortality function, and in particular to the parameter we use to measure the density dependent phage mortality rate. Second, we incorporate spatial effects by deriving, in one spatial dimension, a delay reactiondiffusion model in which the delay term is rigorously derived by solving a von Foerster equation. Using this model, we formally compute the speed at which the viral infection spreads through the domain and investigate how this speed depends on the system parameters. Numerical simulations suggest that the minimum speed according to linear theory is the asymptotic speed of propagation.