一类具有饱和发生率的染病食饵-捕食者随机模型的动力学分析

Dynamic analysis of a infected prey-predator stochastic model with saturation incidence

研究了一类带有饱和发生率和随机比率依赖的HollingⅢ型功能反应的染病食饵捕食者随机模型.首先,利用Itô公式和构造的Lyapunov函数证明了染病食饵捕食者随机模型存在唯一的全局正解.其次,利用Has’miniskii遍历性理论证明了随机模型存在唯一的遍历平稳分布.再次,利用Itô公式、大数定律、鞅理论得到了染病食饵种群的阈值R^(h)_(0):当R^(h)_(0)<1时疾病将趋于灭绝,当R^(h)_(0)>1时疾病将长期存在.最后,利用数值仿真验证了所得结果的正确性.

In this paper,we investigated the dynamics of a stochastic ratio-dependent infected prey-predator model with saturation incidence and Holling-typeⅢfunctional response.Firstly,we proved that the unique solution of stochastic model was globally positive by using Itôformula and constructing Lyapunov function.Secondly,the existence of a unique ergodic stationary distribution was studied by using the ergodicity theory of Hasminiskii.Thirdly,the threshold R^(h)_(0) for the infected prey population was obtained by using Itôformula,the law of large numbers,and the martingale theory,that is,the disease will tend to extinction if R^(h)_(0)<1,and it will exist for a long time if R^(h)_(0)>1.Finally,numerical simulations were used to verify the correctness of the obtained results.