Effects of zooplankton selectivity on phytoplankton in an ecosystem affected by free-viruses and environmental toxins

Saswati Biswas; Pankaj Kumar Tiwari; Yun Kang; Samares Pal; Saswati Biswas; Pankaj Kumar Tiwari; Yun Kang; Samares Pal

doi:10.3934/mbe.2020065

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 2: 1272-1317. doi: 10.3934/mbe.2020065

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Effects of zooplankton selectivity on phytoplankton in an ecosystem affected by free-viruses and environmental toxins

1.
Department of Mathematics, University of Kalyani, Kalyani - 741235, India
2.
Science and Mathematics Faculty, Arizona State University, Mesa, AZ 85212, USA

Received: 01 July 2019 Accepted: 15 November 2019 Published: 20 November 2019

In the present study, we investigate the selective feeding of zooplankton on phytoplankton infected by free-viruses in the presence of environmental toxins in the marine ecosystem. The environmental toxins assume to decrease the growth rate of susceptible phytoplankton, and increase the death rate of infected phytoplankton and zooplankton. Global sensitivity analysis identifies important parameters of the system having crucial impact on the aquatic health. The coexistence equilibrium of the system stabilizes on increasing the parameters related to inhibition of phytoplankton growth due to environmental toxins and the force of infection, and destabilizes on increasing the carrying capacity of susceptible phytoplankton and preference of zooplankton on infected phytoplankton. The chance of extinction of free-viruses increases on increasing the preference of zooplankton on infected phytoplankton or decreasing the force of infection. Moreover, if the input rate of environmental toxins is high, then the system becomes zooplankton-free for higher values of force of infection. On increasing the values of preference of zooplankton on infected phytoplankton, the system exhibits transition from stable coexistence to oscillations around coexistence equilibrium to oscillations around disease-free equilibrium. We observe that the presence of free-viruses and environmental toxins in the system drive zooplankton population to very low equilibrium values but the ecological balance of the aquatic food web can be maintained by modulating the decay (depletion) rate of free-viruses (environmental toxins).
- mathematical model,
- plankton dynamics,
- free-viruses,
- environmental toxins,
- Hopf-bifurcation,
- global sensitivity
Citation: Saswati Biswas, Pankaj Kumar Tiwari, Yun Kang, Samares Pal. Effects of zooplankton selectivity on phytoplankton in an ecosystem affected by free-viruses and environmental toxins[J]. Mathematical Biosciences and Engineering, 2020, 17(2): 1272-1317. doi: 10.3934/mbe.2020065

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Abstract

In the present study, we investigate the selective feeding of zooplankton on phytoplankton infected by free-viruses in the presence of environmental toxins in the marine ecosystem. The environmental toxins assume to decrease the growth rate of susceptible phytoplankton, and increase the death rate of infected phytoplankton and zooplankton. Global sensitivity analysis identifies important parameters of the system having crucial impact on the aquatic health. The coexistence equilibrium of the system stabilizes on increasing the parameters related to inhibition of phytoplankton growth due to environmental toxins and the force of infection, and destabilizes on increasing the carrying capacity of susceptible phytoplankton and preference of zooplankton on infected phytoplankton. The chance of extinction of free-viruses increases on increasing the preference of zooplankton on infected phytoplankton or decreasing the force of infection. Moreover, if the input rate of environmental toxins is high, then the system becomes zooplankton-free for higher values of force of infection. On increasing the values of preference of zooplankton on infected phytoplankton, the system exhibits transition from stable coexistence to oscillations around coexistence equilibrium to oscillations around disease-free equilibrium. We observe that the presence of free-viruses and environmental toxins in the system drive zooplankton population to very low equilibrium values but the ecological balance of the aquatic food web can be maintained by modulating the decay (depletion) rate of free-viruses (environmental toxins).

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