Dynamical behaviors of stochastic eco‐epidemic predator–prey model with Allee effect in prey and Lévy jump

Abstract

In this paper, the dynamical behaviors of a stochastic eco‐epidemic predator–prey model with Lévy jump and Allee effect for prey population are investigated. First, the existence and uniqueness of the global positive solution are built. Then, the long‐term behaviors of the prey and predator populations are obtained. Furthermore, we demonstrate the stochastic ultimate boundedness of all species and the ergodic stationary distribution without Lévy jump. Finally, numerical examples are provided to support the theoretical analysis results.