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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Nutrient and Viral Infection in Phytoplankton Control Planktonic Bloom-conclusion Drawn from a Mathematical Study of Nutrient-Phytoplankton-Zooplankton System

Discontinuity, Nonlinearity, and Complexity 14(1) (2025) 163--177 | DOI:10.5890/DNC.2025.03.010

Krishna Pada Das$^1$, Shubhadeep Ghosh$^2$, Bhagabat Das$^3$, Satyajit Saha$^4$

$^{1}$ Department of Mathematics, Mahadebananda Mahavidyalaya Monirampore, P.O.-Barrackpore, Kolkata-120, India

$^{2}$ Department of Mathematics $&$ Statistics, Umeschandra College, Kolkata-12, West Bengal, India

$^{3}$ Department of Mathematics, Techno International, Batanagar, India

$^{4}$ Department of App. Sc. and Humanities, Shaheed Bhagat Singh State University, Ferozepur, Punjab, India

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Abstract

Present paper deals with a nutrient-phytoplankton-zooplankton model with viral disease in phytoplankton species. We have considered the stability of different equilibria under some threshold conditions. We have worked out the basic reproduction number and we analyzed the community structure by the help of these basic reproduction number. Our observations indicate that as the parameters cross a certain critical value, then the system enters into Hopf bifurcation so the existence of Hopf-bifurcation for the interior equilibrium of the system is explored. To observe the global behaviour of our model system we have performed extensive numerical simulations. From our numerical results it is clear that viral infection and nutrient concentration are responsible for occurrence and control of phytoplankton blooms. The analysis identifies an important threshold effect: a bloom will only be triggered when nutrients exceed a certain definite level. From our numerical studies we see that viral infection is responsible for zooplankton survival and plankton oscillation dynamics and nutrient threshold is required for plankton oscillations and zooplankton survival.

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