Asymptotic behavior and extinction of a stochastic predator-prey model with Holling type II functional response and disease in the prey

被引:1
作者
Ma, Jiying [1 ]
Ren, Haimiao [1 ]
机构
[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China
基金
中国国家自然科学基金;
关键词
asymptotic behavior; environment noise; extinction; stochastic predator-prey model; EPIDEMIC MODEL; STATIONARY DISTRIBUTION; LESLIE-GOWER; DYNAMICS; POPULATIONS; INFECTION; SYSTEM;
D O I
10.1002/mma.8744
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we formulate and investigate a stochastic one-prey and two-predator model with Holling II functional response and disease in the prey, in which the predators only feed on infected prey. The existence and uniqueness of global positive solution is proved by using conventional methods. The corresponding deterministic model has a disease-free equilibrium point if the basic reproduction number R0<1$$ {R}_0, and it has three boundary equilibrium points and one positive equilibrium point if R0>1$$ {R}_0>1 $$. For the stochastic model, we investigate the asymptotic behavior around all of the five equilibrium points and prove that there is a unique ergodic stationary distribution under certain conditions. Moreover, we obtain the condition on which the population of the infected prey and the two predators will die out in the time mean sense. Finally, numerical simulations are conducted to illustrate our analysis results.
引用
收藏
页码:4111 / 4133
页数:23
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