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A stochastic spatial model for the sterile insect control strategy

Publication ,  Journal Article
Huang, X; Durrett, R
Published in: Stochastic Processes and their Applications
March 1, 2023

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.

Duke Scholars

Published In

Stochastic Processes and their Applications

DOI

ISSN

0304-4149

Publication Date

March 1, 2023

Volume

157

Start / End Page

249 / 278

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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Huang, X., & Durrett, R. (2023). A stochastic spatial model for the sterile insect control strategy. Stochastic Processes and Their Applications, 157, 249–278. https://doi.org/10.1016/j.spa.2022.11.018
Huang, X., and R. Durrett. “A stochastic spatial model for the sterile insect control strategy.” Stochastic Processes and Their Applications 157 (March 1, 2023): 249–78. https://doi.org/10.1016/j.spa.2022.11.018.
Huang X, Durrett R. A stochastic spatial model for the sterile insect control strategy. Stochastic Processes and their Applications. 2023 Mar 1;157:249–78.
Huang, X., and R. Durrett. “A stochastic spatial model for the sterile insect control strategy.” Stochastic Processes and Their Applications, vol. 157, Mar. 2023, pp. 249–78. Scopus, doi:10.1016/j.spa.2022.11.018.
Huang X, Durrett R. A stochastic spatial model for the sterile insect control strategy. Stochastic Processes and their Applications. 2023 Mar 1;157:249–278.
Journal cover image

Published In

Stochastic Processes and their Applications

DOI

ISSN

0304-4149

Publication Date

March 1, 2023

Volume

157

Start / End Page

249 / 278

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0104 Statistics
  • 0102 Applied Mathematics