On the Dynamics of a Stochastic Ratio-Dependent Predator-Prey System with Infection for the Prey  

作　　者：Jiying Ma Haimiao Ren Jiying Ma;Haimiao Ren(College of Science, University of Shanghai for Science and Technology, Shanghai, China;Department of Mathematics, University of Shanghai for Science and Technology, Shanghai, China)

机构地区：[1]College of Science, University of Shanghai for Science and Technology, Shanghai, China [2]Department of Mathematics, University of Shanghai for Science and Technology, Shanghai, China

出　　处：《Open Journal of Applied Sciences》2021年第4期440-457,共18页应用科学（英文）

摘　　要：In this paper, we investigate the dynamics of a stochastic predator-prey model with ratio-dependent functional response and disease in the prey. Firstly, we prove the existence and uniqueness of the positive solution for the stochastic model by using conventional methods. Then we obtain the threshold <img alt="" src="Edit_0a62b9be-7934-457b-aca3-af3420f5b5ee.png" /> for the infected prey population, that is, the disease will tend to extinction if <img alt="" src="Edit_e6cd63f6-de07-42be-a22a-8750d6c8aac9.png" />< 1, and it will exist in the long time if  <img alt="" src="Edit_5964fdd8-a9fe-4dc2-b897-f4206f046f65.png" />> 1. Finally, the sufficient condition on the existence of a unique ergodic stationary distribution is obtained, which indicates that all the populations are permanent in the time mean sense. Numerical simulations are conducted to verify our analysis results.In this paper, we investigate the dynamics of a stochastic predator-prey model with ratio-dependent functional response and disease in the prey. Firstly, we prove the existence and uniqueness of the positive solution for the stochastic model by using conventional methods. Then we obtain the threshold <img alt="" src="Edit_0a62b9be-7934-457b-aca3-af3420f5b5ee.png" /> for the infected prey population, that is, the disease will tend to extinction if <img alt="" src="Edit_e6cd63f6-de07-42be-a22a-8750d6c8aac9.png" />< 1, and it will exist in the long time if  <img alt="" src="Edit_5964fdd8-a9fe-4dc2-b897-f4206f046f65.png" />> 1. Finally, the sufficient condition on the existence of a unique ergodic stationary distribution is obtained, which indicates that all the populations are permanent in the time mean sense. Numerical simulations are conducted to verify our analysis results.

关 键 词：Stochastic Predator-Prey Model RATIO-DEPENDENT Stationary Distribution EXTINCTION 

分 类 号：O17[理学—数学]