Advances in Applied Probability

Growth of a population of bacteria in a dynamical hostile environment

Olivier Garet and Régine Marchand

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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.

Article information

Adv. in Appl. Probab., Volume 46, Number 3 (2014), 661-686.

First available in Project Euclid: 29 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35]

Contact process directed percolation renormalization random environment stochastic domination block construction interacting particle system


Garet, Olivier; Marchand, Régine. Growth of a population of bacteria in a dynamical hostile environment. Adv. in Appl. Probab. 46 (2014), no. 3, 661--686. doi:10.1239/aap/1409319554.

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