A stochastic spatial model for the sterile insect control strategy

Xiangying Huang and Rick Durrett

Stochastic Processes and their Applications, 2023, vol. 157, issue C, 249-278

Abstract: In the system we study, 1’s and 0’s represent occupied and vacant sites in the contact process with births at rate λ and deaths at rate 1. −1’s are sterile individuals that do not reproduce but appear spontaneously on vacant sites at rate α and die at rate θα. We show that the system (which is attractive but has no dual) dies out at the critical value and has a nontrivial stationary distribution when it is supercritical. Our most interesting results concern the asymptotics when α→0. In this regime the process resembles the contact process in a random environment.

Keywords: Contact process; Random environment; Block construction; Shape theorem (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2022.11.018

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