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 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 . It persists when The case does not allow for knowing whether the population goes extinct or not.