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Extinction and persistence in a stochastic Nicholson’s model of blowfly population with delay and Lévy noise

Author

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  • Layla Basri
  • Driss Bouggar
  • Mohamed El Fatini
  • Mohamed El Khalifi
  • Aziz Laaribi

Abstract

Existence and uniqueness of a global positive solution are proved for a stochastic Nicholson’s equation of a blowfly population with delay and Lévy noise. The first-order moment of the solution is bounded and the mean of its second moment is finite. A threshold quantity $${{\cal T}\!_j}$$Tj depending on the parameters is involved in the drift, the diffusion parameter, and the magnitude and distribution of jumps. The blowfly population goes extinct exponentially fast when $${{\cal T}\!_j} \lt 1$$Tj 1. The case $${{\cal T}\!_s} = 1$$Ts=1 does not allow for knowing whether the population goes extinct or not.

Suggested Citation

  • Layla Basri & Driss Bouggar & Mohamed El Fatini & Mohamed El Khalifi & Aziz Laaribi, 2023. "Extinction and persistence in a stochastic Nicholson’s model of blowfly population with delay and Lévy noise," Mathematical Population Studies, Taylor & Francis Journals, vol. 30(4), pages 209-228, October.
    • Handle: RePEc:taf:mpopst:v:30:y:2023:i:4:p:209-228
    DOI: 10.1080/08898480.2023.2165338
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