Analysis Of Stochastic Predator-prey Models With Lévy Noise And Eco-epidemic

In recent years,the theory of stochastic differential equations has been deeply applied in the field of biomathematics,and the use of stochastic differential equations to construct suitable mathematical models can better help scholars to understand population size changes and population development,which provides effective theoretical support to maintain the balanced development of biological populations.Natural organisms are inevitably affected by environmental noise,and the perturbation of environmental noise will change the population size.While Lévy noise must be taken into account when describing a violent,intermittent perturbation,white noise is used to describe a small,continuous perturbation.Meanwhile,diseases can spread among species,so it is more practical to consider to introduce infectious disease factors into the predator-prey model with environmental perturbations.The main research of this paper is divided into two aspects as follows:(1)We studied prey populations with Allee effects,transmission of infectious diseases between predator populations,and white noise and Lévy noise effects in a predator-prey model.First,the paper proves the existence of unique global positive solutions of the model,then discusses the conditions that the system is extinct,persists in a time-averaged for these properties to occur,and considers the conditions for the existence of an ergodic stationary distribution of the system when the population system is not subject to drastic environmental changes.Finally,numerical simulations with suitable parameters are selected to verify the validity of the conclusions.(2)We studied prey populations suffering fear effects,transmission of infectious diseases between prey populations,and with white noise and Lévy noise effects of the predator-prey model.First,this paper proves the existence of a unique global positive solution of the system,then discusses the conditions for the population extinction,the persistence of this system in time-averaged sense,then considers the solution of the system with stochastic ultimate boundedness and ergodic stationary distribution when the system is not subject to drastic environmental changes,i.e.,not affected by Lévy noise,and finally verifies the correctness of the obtained conditions by simulating the trajectory of the solution with suitably chosen values.