Competition between growths governed by Bernoulli Percolation

We study a competition model on ${\mathbb{Z}}^d$ where the two infections are driven by supercritical Bernoulli percolations with distinct parameters $p$ and $q$. We prove that, for any $q$, there exist at most countably many values of $p<\min (q,\overrightarrow{p\mathrm{\_}c})$ such that coexistence can occur.