Growth of a population of bacteria in a dynamical hostile environment

Olivier Garet (1) , Régine Marchand (1)

1 IECL - Institut Élie Cartan de Lorraine

We study the growth of a population of bacteria in a dynamical hostile environment corresponding to the immune system of the colonised 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. For appropriate values of the parameters, we prove that the population of bacteria grows linearly. In this perspective, we build general tools to study dependent percolation models issued from renormalization processes.

Mots clés: block construction; random environment; stochastic domination; contact process; directed percolation; renormalization; interacting particle system

Domaines: Probabilités [math.PR]

Olivier Garet, Régine Marchand. Growth of a population of bacteria in a dynamical hostile environment. Advances in Applied Probability, 2014, 46 (3), pp.661-686. ⟨10.1239/aap/1409319554⟩. ⟨hal-00528471v3⟩