A stochastic $n$-species marine food chain model with harvesting and Lévy noises is proposed. First, the criterion on the asymptotic stability in distribution is established. Second, the criterion on the existence of optimal harvesting strategy (OHS) and the maximum of expectation of sustainable yield (MESY) are derived. Furthermore, the numerical simulations are presented to verify the theoretical results. Our results show that (i) noises intensity can easily affect the dynamics of marine populations, leading to the imbalances of marine ecology, (ii) the establishment of an optimal harvesting strategy should fully consider the impact of noises intensity for better managing and protecting marine resources.

The paper studies the global dynamics and probability density function for a class of stochastic SVI epidemic models with white noise, Lévy jumps and nonlinear incidence. The stability of disease-free and endemic equilibria for the corresponding deterministic model is first obtained. The threshold criteria on the stochastic extinction, persistence and stationary distribution are established. That is, the disease is extinct with probability one if the threshold value $R_0^s<1$, and the disease is persistent in the mean and any positive solution is ergodic and has a unique stationary distribution if $R_0^s>1$. Furthermore, the approximate expression of the log-normal probability density function around the quasi-endemic equilibrium of the stochastic model is calculated. A new technique for the calculation of the probability density function is proposed. Lastly, the numerical examples and simulations are presented to verify the main results.