A stochastic spatial model for the sterile insect control strategy

TL;DR

This paper introduces a stochastic spatial model simulating sterile insect control, analyzing its extinction and stationary behavior, especially as the sterile release rate approaches zero, revealing similarities to contact processes in random environments.

Contribution

It develops a novel stochastic spatial model for sterile insect control and analyzes its critical and supercritical regimes, including asymptotic behavior as sterile release rate diminishes.

Findings

System dies out at critical value

Nontrivial stationary distribution exists in supercritical regime

Asymptotic behavior resembles contact process in random environment

Abstract

In the system we study, 1's and 0's represent occupied and vacant sites in the contact process with births at rate $\lambda$ and deaths at rate 1. $-1$'s are sterile individuals that do not reproduce but appear spontaneously on vacant sites at rate $\alpha$ and die at rate $\theta\alpha$. 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 $\alpha\to 0$. In this regime the process resembles the contact process in a random environment.