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

Layla Basri, Driss Bouggar, Mohamed El Fatini, Mohamed El Khalifi and Aziz Laaribi

Mathematical Population Studies, 2023, vol. 30, issue 4, 209-228

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.

Date: 2023
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DOI: 10.1080/08898480.2023.2165338

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