Survival analysis of an impulsive stochastic delay logistic model with Lévy jumps

This paper studies a stochastic delay logistic model with Levy jumps and impulsive perturbations. We show that the model has a unique global positive solution. Sufficient conditions for extinction, non-persistence in the mean, weak persistence, stochastic permanence and global asymptotic stability are established. The threshold between weak persistence and extinction is obtained. The results demonstrate that impulsive perturbations which may represent human factor play an important role in protecting the population even if it suffers sudden environmental shocks that can be discribed by Levy jumps.