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

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 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 Tj<1. It persists when Tj>1. The case Ts=1 does not allow for knowing whether the population goes extinct or not.