Spread of viral infection of immobilized bacteria

Don A. Jones; Hal L. Smith; Horst R. Thieme

doi:10.3934/nhm.2013.8.327

Article Contents

2013, Volume 8, Issue 1: 327-342. Doi: 10.3934/nhm.2013.8.327

This issue Previous Article The existence and uniqueness of unstable eigenvalues for stripe patterns in the Gierer-Meinhardt system Next Article Wavespeed selection in the heterogeneous Fisher equation: Slowly varying inhomogeneity

Spread of viral infection of immobilized bacteria

1.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA 85287
2.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804
3.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287

Received: April 2012

Revised: October 2012

Published: March 2013

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Abstract

A reaction diffusion system with a distributed time delay is proposed for virus spread on bacteria immobilized on an agar-coated plate. A distributed delay explicitly accounts for a virus latent period of variable duration. The model allows the number of virus progeny released when an infected cell lyses to depend on the duration of the latent period. A unique spreading speed for virus infection is established and traveling wave solutions are shown to exist.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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