Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model
Abstract This paper formulates an infected predator-prey model with Beddington-DeAngelis functional response from a classical deterministic framework to a stochastic differential equation (SDE). First, we provide a global analysis including the global positive solution, stochastically ultimate bound...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1265-z |
| _version_ | 1818496656037904384 |
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| author | Tao Feng Xinzhu Meng Lidan Liu Shujing Gao |
| author_facet | Tao Feng Xinzhu Meng Lidan Liu Shujing Gao |
| author_sort | Tao Feng |
| collection | DOAJ |
| description | Abstract This paper formulates an infected predator-prey model with Beddington-DeAngelis functional response from a classical deterministic framework to a stochastic differential equation (SDE). First, we provide a global analysis including the global positive solution, stochastically ultimate boundedness, the persistence in mean, and extinction of the SDE system by using the technique of a series of inequalities. Second, by using Itô’s formula and Lyapunov methods, we investigate the asymptotic behaviors around the equilibrium points of its deterministic system. The solution of the stochastic model has a unique stationary distribution, it also has the characteristics of ergodicity. Finally, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients to illustrate the performance of the theoretical results. The results show that if the intensity of the disturbance is sufficiently large, the persistence of the SDE model can be destroyed. |
| first_indexed | 2024-12-10T18:35:34Z |
| format | Article |
| id | doaj.art-d0f6fbcd90944a379925ad1acb621e38 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-10T18:35:34Z |
| publishDate | 2016-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d0f6fbcd90944a379925ad1acb621e382022-12-22T01:37:49ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-12-012016112910.1186/s13660-016-1265-zApplication of inequalities technique to dynamics analysis of a stochastic eco-epidemiology modelTao Feng0Xinzhu Meng1Lidan Liu2Shujing Gao3College of Mathematics and Systems Science, Shandong University of Science and TechnologyCollege of Mathematics and Systems Science, Shandong University of Science and TechnologyCollege of Mathematics and Systems Science, Shandong University of Science and TechnologyKey Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal UniversityAbstract This paper formulates an infected predator-prey model with Beddington-DeAngelis functional response from a classical deterministic framework to a stochastic differential equation (SDE). First, we provide a global analysis including the global positive solution, stochastically ultimate boundedness, the persistence in mean, and extinction of the SDE system by using the technique of a series of inequalities. Second, by using Itô’s formula and Lyapunov methods, we investigate the asymptotic behaviors around the equilibrium points of its deterministic system. The solution of the stochastic model has a unique stationary distribution, it also has the characteristics of ergodicity. Finally, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients to illustrate the performance of the theoretical results. The results show that if the intensity of the disturbance is sufficiently large, the persistence of the SDE model can be destroyed.http://link.springer.com/article/10.1186/s13660-016-1265-zstochastic eco-epidemiology modelHölder inequality and Chebyshev inequalityasymptotic behaviorpersistence in meanstationary distribution |
| spellingShingle | Tao Feng Xinzhu Meng Lidan Liu Shujing Gao Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model Journal of Inequalities and Applications stochastic eco-epidemiology model Hölder inequality and Chebyshev inequality asymptotic behavior persistence in mean stationary distribution |
| title | Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model |
| title_full | Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model |
| title_fullStr | Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model |
| title_full_unstemmed | Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model |
| title_short | Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model |
| title_sort | application of inequalities technique to dynamics analysis of a stochastic eco epidemiology model |
| topic | stochastic eco-epidemiology model Hölder inequality and Chebyshev inequality asymptotic behavior persistence in mean stationary distribution |
| url | http://link.springer.com/article/10.1186/s13660-016-1265-z |
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