Extinction and survival in inherited sterility

Abstract

We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on ${\mathbb{Z}}^d$ according to a contact process with parameter $\hat{I}»>0$. With probability $p\in [0,1]$ an offspring is fertile and can give birth to other individuals at rate $\hat{I}»$. With probability $1-p$, an offspring is sterile and blocks the site it sits on until it dies. The goal is to prove that at fixed $\hat{I}»$, the system survives for large enough $p$ and dies out for small enough $p$. The model is not attractive, since an increase of fertile individuals potentially causes that of sterile ones. However, thanks to a comparison argument with attractive models, we are able to answer our question.

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