Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System
It is well known that the evolution of natural populations is almost inevitably disturbed by various environmental factors. Various experiments have shown that the growth of phytoplankton might be affected by nutrient availability, water temperature, and light, while the development of zooplankton i...
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/8/1218 |
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| author | Xiaomei Feng Yuan Miao Shulin Sun Lei Wang |
| author_facet | Xiaomei Feng Yuan Miao Shulin Sun Lei Wang |
| author_sort | Xiaomei Feng |
| collection | DOAJ |
| description | It is well known that the evolution of natural populations is almost inevitably disturbed by various environmental factors. Various experiments have shown that the growth of phytoplankton might be affected by nutrient availability, water temperature, and light, while the development of zooplankton is more disturbed by the pH value of the seawater, water temperature, and water movement. However, it is not clear how these environmental fluctuations affect the dynamical behavior of the phytoplankton and zooplankton system. In this paper, a stochastic eco-epidemiological model for viral infection in the toxin-producing phytoplankton and zooplankton system is proposed. Firstly, the existence and uniqueness of globally positive solutions for this model is shown. Secondly, the stochastic boundedness of solutions for the model is proved. Moreover, sufficient conditions for the extinction and persistence in the mean for the phytoplankton and zooplankton are obtained by constructing appropriate stochastic Lyapunov functions and using analytical techniques. Numerical simulations are carried out to demonstrate different dynamical behaviors including coexistence, extinction of the whole plankton system, partial persistence and extinction, and their corresponding probability density curves. |
| first_indexed | 2024-03-09T10:32:27Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:32:27Z |
| publishDate | 2022-04-01 |
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| spelling | doaj.art-cbbb4b8d9ce34e6c9ce3fdd57b5aa4f12023-12-01T21:11:55ZengMDPI AGMathematics2227-73902022-04-01108121810.3390/math10081218Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton SystemXiaomei Feng0Yuan Miao1Shulin Sun2Lei Wang3School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, ChinaSchool of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, ChinaSchool of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, ChinaDepartment of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, ChinaIt is well known that the evolution of natural populations is almost inevitably disturbed by various environmental factors. Various experiments have shown that the growth of phytoplankton might be affected by nutrient availability, water temperature, and light, while the development of zooplankton is more disturbed by the pH value of the seawater, water temperature, and water movement. However, it is not clear how these environmental fluctuations affect the dynamical behavior of the phytoplankton and zooplankton system. In this paper, a stochastic eco-epidemiological model for viral infection in the toxin-producing phytoplankton and zooplankton system is proposed. Firstly, the existence and uniqueness of globally positive solutions for this model is shown. Secondly, the stochastic boundedness of solutions for the model is proved. Moreover, sufficient conditions for the extinction and persistence in the mean for the phytoplankton and zooplankton are obtained by constructing appropriate stochastic Lyapunov functions and using analytical techniques. Numerical simulations are carried out to demonstrate different dynamical behaviors including coexistence, extinction of the whole plankton system, partial persistence and extinction, and their corresponding probability density curves.https://www.mdpi.com/2227-7390/10/8/1218stochastic plankton modelviral infectionstochastic boundednessextinction and persistence in the mean |
| spellingShingle | Xiaomei Feng Yuan Miao Shulin Sun Lei Wang Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System Mathematics stochastic plankton model viral infection stochastic boundedness extinction and persistence in the mean |
| title | Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System |
| title_full | Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System |
| title_fullStr | Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System |
| title_full_unstemmed | Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System |
| title_short | Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System |
| title_sort | dynamic behaviors of a stochastic eco epidemiological model for viral infection in the toxin producing phytoplankton and zooplankton system |
| topic | stochastic plankton model viral infection stochastic boundedness extinction and persistence in the mean |
| url | https://www.mdpi.com/2227-7390/10/8/1218 |
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