ABSTRACT We study the contact process on the long‐range percolation cluster on where each edge is open with probability for . Using a renormalization procedure, we apply the Peierls‐type argument to prove that the contact process dies out if the transmission rate is lower than a critical threshold. Our methods involve the control of crossing probabilities for percolation on randomly‐stretched lattices as in Hilário et al.
Gomes et al. (Sun,) studied this question.