A delay reaction-diffusion model of the spread of bacteriophage infection

Stephen A. Gourley, Yang Kuang

Research output: Contribution to journalArticlepeer-review

66 Scopus citations

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 reaction-diffusion 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.

Original languageEnglish (US)
Pages (from-to)550-566
Number of pages17
JournalSIAM Journal on Applied Mathematics
Volume65
Issue number2
DOIs
StatePublished - 2005

Keywords

  • Delay
  • Reaction-diffusion
  • Stage structure
  • Through-stage death rate
  • Traveling wave

ASJC Scopus subject areas

  • Applied Mathematics

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