[SS05] Data and model driven - study on infectious diseases modelling

[SS05-03] Stochastic effects on a discrete crop-pest-natural enemy model

*Bing Liu¹ (1. Anshan Normal University (China))

Keywords:

Crop-pest-natural enemy model,Stochastic discrete model

Considering that the discrete model maintains the stability of the equilibrium point of the original continuous model and that the standard discrete numerical method is dependent on the selection of time step in the calculation process, in this talk, we establish a stochastic discrete crop-pest-natural enemy model based on the non-standard finite difference method, and discuss the stability conditions of the equilibria of the deterministic discrete model. By studying the asymptotic mean square stability of the zero solution of the linear stochastic discrete model, the sufficient conditions for the stability in probability of the nonlinear stochastic discrete model at the equilibrium point of pest extinction and the positive equilibrium point are obtained, and the effects of stochastic noise on pest control strategy are given. By numerical simulation, the sensitivity of Euler method and nonstandard finite difference method to time step is compared and analyzed.