Complete convergence theorem for a two-level contact process

Abstract

We study a two-level contact process. We think of fleas living on a species of animals. The animals are a supercritical contact process in ${\mathbb{Z}}^d$. The contact process acts as the random environment for the fleas. The fleas do not affect the animals, give birth at rate $\mu$ when they are living on a host animal, and die at rate $\delta$ when they do not have a host animal. The main result is that if the contact process is supercritical and the fleas survive then the complete convergence theorem holds. This is done using a block construction so as a corollary we conclude that the fleas die out at their critical value.

References in corpus (4)

• The contact process in a dynamic random environment
• Stochastic domination for a hidden Markov chain with applications to the contact process in a randomly evolving environment
• Stochastic spatial models of host-pathogen and host-mutualist interactions I
• The critical contact process in a randomly evolving environment dies out