Spread of viral infection of immobilized bacteria

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

doi:10.3934/nhm.2013.8.327

Networks and Heterogeneous Media

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

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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: 01 April 2012 Revised: 01 October 2012
Primary: 58F15, 58F17; Secondary: 53C35.

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.
- Virus plaque,
- virus spread,
- traveling wave solution,
- speed of spread,
- linear determinacy,
- distributed delay
Citation: Don A. Jones, Hal L. Smith, Horst R. Thieme. Spread of viral infection of immobilized bacteria[J]. Networks and Heterogeneous Media, 2013, 8(1): 327-342. doi: 10.3934/nhm.2013.8.327

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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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