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A Delay Reaction-Diffusion Model of the Spread of Bacteriophage Infection

Gourley, S A and Kuang, Y (2005) A Delay Reaction-Diffusion Model of the Spread of Bacteriophage Infection SIAM Journal on Applied Mathematics, 65 (2). pp. 550-566. ISSN 00361399

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Abstract

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.

Item Type: Article
Additional Information: Published in <i>SIAM Journal on Applied Mathematics,</i> Vol. 65, Iss. 2, pp. 550 - 566. Copyright 2005 SIAM Publications. <br>Click <a href=http://www.siam.org/journals/siap.php >here</a> to access the journal's website.</br>
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:40
Last Modified: 23 Sep 2013 18:32
URI: http://epubs.surrey.ac.uk/id/eprint/1399

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