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A stochastic spatial model for the sterile insect control strategy

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  • Huang, Xiangying
  • Durrett, Rick

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.

Suggested Citation

  • Huang, Xiangying & Durrett, Rick, 2023. "A stochastic spatial model for the sterile insect control strategy," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 249-278.
    • Handle: RePEc:eee:spapps:v:157:y:2023:i:c:p:249-278
    DOI: 10.1016/j.spa.2022.11.018
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    References listed on IDEAS

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    1. Cristali, Irina & Junge, Matthew & Durrett, Rick, 2020. "Poisson percolation on the oriented square lattice," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 488-502.
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