PMID: 22587127May 17, 2012Paper

Predator-prey dynamics in a uniform medium lead to directed percolation and wave-train propagation

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Alexandra Agranovich, Yoram Louzoun

Abstract

The dynamics of birth-death processes with extinction points that are unstable in the deterministic average description has been extensively studied, mainly in the context of the stochastic transition from the mean-field attracting fixed point to the absorbing state. Here we study the opposite case of a small perturbation from the zero-population absorbing state. We show that such perturbations can grow beyond the mean-field attracting fixed point and then can collapse back into the absorbing state. Such dynamics can represent, for example, the fast growth of a pathogen and then its destruction by the immune system. We show that when the prey perturbation extinction probability is high, the loss of synchronization between the prey densities in different regions in space leads to two possible dynamic regimes: (a) a directed percolation regime based on the balance between regions escaping the absorbing state and regions absorbed into it, and (b) wave trains representing the transition of the entire space to the mean-field stable positive fixed point.

References

Dec 15, 1986·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·R M Anderson, R M May
Jan 1, 1986·Bulletin of Mathematical Biology·H I Freedman, G S Wolkowicz
Sep 7, 1995·Journal of Theoretical Biology·U DieckmannR Law
May 1, 1996·The Journal of Experimental Medicine·M F BachmannR M Zinkernagel
Jan 1, 1996·Journal of Mathematical Biology·U Dieckmann, R Law
Oct 22, 1998·Theoretical Population Biology· de Roos AMW G Wilson
May 19, 1997·The American Journal of Medicine·M P Busch, G A Satten
Dec 2, 1996·Physical Review Letters·J Cardy, U C Täuber
Mar 5, 1999·Immunology Letters·D H Busch, E G Pamer
May 29, 2000·Bulletin of Mathematical Biology·W S Gurney, A R Veitch
Aug 30, 2000·Proceedings of the National Academy of Sciences of the United States of America·N M ShnerbS Solomon
Apr 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N M ShnerbS Solomon
May 17, 2003·Bulletin of Mathematical Biology·Yoram LouzounIrun R Cohen
Sep 30, 2003·Nature Immunology·Arup K ChakrabortyAndrey S Shaw
Oct 8, 2003·The Journal of Immunology : Official Journal of the American Association of Immunologists·Rob J De BoerAlan S Perelson
Nov 1, 2003·Veterinary Immunology and Immunopathology·M RambeaudS P Oliver
Nov 11, 2003·Trends in Microbiology·Sebastian BonhoefferViktor Müller
Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Beth A ReidJason C Brunson
Dec 20, 2003·Physical Review Letters·M A TsyganovV N Biktashev
Mar 25, 2004·Journal of Theoretical Biology·Gábor Domokos, István Scheuring
May 14, 2004·Theoretical Population Biology·Cheryl J Briggs, Martha F Hoopes
Aug 28, 2004·Journal of Virology·Miles P DavenportAlan S Perelson
Oct 2, 2004·Nature Reviews. Immunology·Eric G Pamer
Dec 17, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Vlad Elgart, Alex Kamenev
Jan 5, 2005·Comptes rendus biologies·Roger ArditiChristian Jost
Jan 18, 2006·Journal of Theoretical Biology·Alexandra AgranovichSasi Moalem
Jun 1, 1922·Proceedings of the National Academy of Sciences of the United States of America·A J Lotka
Apr 21, 2006·Mathematical Biosciences·Ryszard Rudnicki, Katarzyna Pichór
May 23, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Mauro MobiliaUwe C Täuber
Jul 15, 2006·Journal of Virology·Prasith BaccamAlan S Perelson
Oct 19, 2006·Experimental and Molecular Pathology·Saumya PandeyDevendra K Agrawal
Jan 24, 2007·Proceedings of the National Academy of Sciences of the United States of America·Roland R RegoesRustom Antia
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Refael Abta, Nadav M Shnerb
Aug 22, 2007·The Journal of Immunology : Official Journal of the American Association of Immunologists·Christian L AlthausRob J De Boer
Oct 4, 2007·The Journal of Immunology : Official Journal of the American Association of Immunologists·Vitaly V Ganusov
Jan 24, 2008·Journal of the Royal Society, Interface·Jonathan A Sherratt, Matthew J Smith
Feb 1, 2008·Physical Review Letters·Kazumasa A TakeuchiMasaki Sano
Sep 26, 2008·Journal of Virology·Vitaly V Ganusov, Rob J De Boer
Dec 31, 2008·Physical Review Letters·Ulrich Dobramysl, Uwe C Täuber
Apr 4, 2009·Ecology·Richard LawJulia L Blanchard
May 6, 2009·The Journal of Immunology : Official Journal of the American Association of Immunologists·Marie SchaefferEllen A Robey
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Baruch Meerson, Pavel V Sasorov

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Citations

Aug 3, 2013·Mathematical Biosciences and Engineering : MBE·Hilla BeharYoram Louzoun
Jul 25, 2014·Theoretical Population Biology·Hilla BeharYoram Louzoun

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