LG–Holling type II diseased predator ecosystem with Lévy noise and white noise

This paper considers an LG–Holling type II diseased predator ecosystem with Lévy noise and white noise. In this prey–predator system, assuming that the predator population is infected by disease and divided into two classes: susceptible predator and infected predator, we show that the system has a unique global positive solution. We investigate the persistence in the mean and extinction for the population, obtain threshold conditions of extinction, persistence in the mean by Itô's formula and a comparison theorem for the stochastic system. In addition, we discuss the uniform boundedness of pth moment with $p>0$ and reveal the stochastically ultimate boundedness of the system. Finally, some numerical simulations are introduced to illustrate our analytical findings.