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Growth of a Population of Bacteria in a Dynamical Hostile Environment

Part of: Equilibrium statistical mechanics Special processes

Published online by Cambridge University Press:  22 February 2016

Olivier Garet  and
Régine Marchand
Olivier Garet*
Affiliation:
Université de Lorraine
Régine Marchand*
Affiliation:
Université de Lorraine
*
∗ Postal address: Université de Lorraine, Institut Élie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506, France.
∗ Postal address: Université de Lorraine, Institut Élie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506, France.
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Abstract

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We study the growth of a population of bacteria in a dynamical hostile environment corresponding to the immune system of the colonized organism. The immune cells evolve as subcritical open clusters of oriented percolation and are perpetually reinforced by an immigration process, while the bacteria try to grow as a supercritical oriented percolation in the remaining empty space. We prove that the population of bacteria grows linearly when it survives. From this perspective, we build general tools to study dependent oriented percolation models issued from renormalization processes.

Keywords

Contact processdirected percolationrenormalizationrandom environmentstochastic dominationblock constructioninteracting particle system

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82B43: Percolation
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 3 , September 2014 , pp. 661 - 686
Copyright
© Applied Probability Trust 

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