Dynamical behavior of a stochastic predator-prey model with Holling-type III functional response and infectious predator

Chuangliang Qin; Jinji Du; Yuanxian Hui; Chuangliang Qin; Jinji Du; Yuanxian Hui

doi:10.3934/math.2022413

AIMS Mathematics

2022, Volume 7, Issue 5: 7403-7418. doi: 10.3934/math.2022413

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Dynamical behavior of a stochastic predator-prey model with Holling-type III functional response and infectious predator

1.
School of Mathematics and Statistics, Xinyang College, Xinyang 464000, China
2.
School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China

Received: 17 November 2021 Revised: 12 January 2022 Accepted: 25 January 2022 Published: 11 February 2022
MSC : 34K20, 34D05, 92B05, 92D25

In this paper, we formulate a stochastic predator-prey model with Holling III type functional response and infectious predator. By constructing Lyapunov functions, we prove the global existence and uniqueness of the positive solution of the model, and establish the ergodic stationary distribution of the positive solution, which indicates that both the prey and predator will coexist for a long time. We also obtain sufficient conditions for the extinction of the predator and prey population. We finally provide numerical simulations to demonstrate our main results.
- stochastic predator-prey model,
- stationary distribution and ergodicity,
- extinction,
- Holling-type III functional response
Citation: Chuangliang Qin, Jinji Du, Yuanxian Hui. Dynamical behavior of a stochastic predator-prey model with Holling-type III functional response and infectious predator[J]. AIMS Mathematics, 2022, 7(5): 7403-7418. doi: 10.3934/math.2022413

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Abstract

In this paper, we formulate a stochastic predator-prey model with Holling III type functional response and infectious predator. By constructing Lyapunov functions, we prove the global existence and uniqueness of the positive solution of the model, and establish the ergodic stationary distribution of the positive solution, which indicates that both the prey and predator will coexist for a long time. We also obtain sufficient conditions for the extinction of the predator and prey population. We finally provide numerical simulations to demonstrate our main results.

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