Analysis of a general stochastic non-autonomous logistic model with delays and Lévy jumps

In this paper, a general stochastic non-autonomous logistic model with delays and Lévy jumps is proposed and studied. Sufficient criteria for extinction, non-persistence in the mean and weak persistence of the model are established. The threshold between weak persistence and extinction is also obtained. Finally, numerical simulations are introduced to illustrate the theoretical analysis results. Our results illustrate that both persistence and extinction have close relationships with time-dependent delay and Lévy noise.