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Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System

Author

Listed:
  • Xiaomei Feng

    (School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, China)

  • Yuan Miao

    (School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China)

  • Shulin Sun

    (School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China)

  • Lei Wang

    (Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China)

Abstract

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.

Suggested Citation

  • Xiaomei Feng & Yuan Miao & Shulin Sun & Lei Wang, 2022. "Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System," Mathematics, MDPI, vol. 10(8), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1218-:d:789288
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    References listed on IDEAS

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    1. Jed A. Fuhrman, 1999. "Marine viruses and their biogeochemical and ecological effects," Nature, Nature, vol. 399(6736), pages 541-548, June.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    3. Jang, Sophia R.-J. & Allen, Edward J., 2015. "Deterministic and stochastic nutrient-phytoplankton- zooplankton models with periodic toxin producing phytoplankton," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 52-67.
    4. Chen, Zhewen & Tian, Zhuyan & Zhang, Shuwen & Wei, Chunjin, 2020. "The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    5. Liu, Chao & Yu, Longfei & Zhang, Qingling & Li, Yuanke, 2018. "Dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 115-137.
    6. Ji, Chunyan & Jiang, Daqing & Lei, Dongxia, 2019. "Dynamical behavior of a one predator and two independent preys system with stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 649-664.
    7. Chunjin Wei & Yingjie Fu, 2020. "Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems," Complexity, Hindawi, vol. 2020, pages 1-15, January.
    8. Yong Wang & Hongbin Wang, 2014. "Stability and Selective Harvesting of a Phytoplankton-Zooplankton System," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, May.
    9. Yu, Xingwang & Yuan, Sanling & Zhang, Tonghua, 2019. "Survival and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 249-264.
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