Mathematical Model for The Dynamics of Nutrient-Phytoplankton System with Delay Under Climate Change and Deoxygination of Oceans

• Author(s): Usman Solomon Alani; Ibrahim Isa Adamu; Shamtang Benshak Musa
• Paper ID: 1719581
• Page: 793-825
• Published Date: 08-07-2026
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 10 Issue 1 July-2026
• DOI: https://doi.org/10.64388/IREV10I1-1719581

Abstract

Marine plankton ecosystems are fundamental to global oxygen production and carbon sequestration, yet they are increasingly threatened by ocean deoxygenation, and climate change. This study proposes a novel six-dimensional delayed differential equation model that captures the complex interactions among nutrient concentration (N), phytoplankton biomass (P), zooplankton biomass (Z), dissolved oxygen (O), upper ocean temperature (T), and greenhouse gas concentration (G). Three discrete time delays account for phytoplankton decomposition, zooplankton decomposition, and toxin maturation in phytoplankton. Existence and uniqueness of solutions are established using the Lipschitz condition. Positivity of solutions and boundedness in a positively invariant region are rigorously proved via comparison theorems, while local asymptotic stability of coexistence and temperature-zero equilibria is proven via linearization and the Routh-Hurwitz criteria. Numerical simulations reveal that baseline parameters induce rapid deoxygenation, with dissolved oxygen falling below 0.5 ppm within 15 days despite an initial phytoplankton bloom. Two scenarios sustain high dissolved oxygenation: (i) fixing temperature at 0 °C, which eliminates warming-induced oxygen loss and thermal inhibition of phytoplankton, and (ii) a minimal-deoxygenation case featuring enhanced photosynthetic production, reduced decomposition demand, and efficient greenhouse gas removal. In contrast, moderate and severe deoxygenation scenarios produce hypoxic conditions or complete plankton collapse. Notably, the selected delays (2.5, 4.0, 5.5 days) do not qualitatively alter long-term dynamics compared to delay-free simulations. These findings provide quantitative thresholds for preventing catastrophic dissolved oxygen depletion and highlight the critical roles of thermal stress and nutrient management in preserving marine ecosystem resilience under climate change.

Keywords

Anoxic, Climate Change, Deoxygenation, Hypoxic, Plankton.

Citations

IRE Journals:
Usman Solomon Alani, Ibrahim Isa Adamu, Shamtang Benshak Musa "Mathematical Model for The Dynamics of Nutrient-Phytoplankton System with Delay Under Climate Change and Deoxygination of Oceans" Iconic Research And Engineering Journals Volume 10 Issue 1 2026 Page 793-825 https://doi.org/10.64388/IREV10I1-1719581

IEEE:
Usman Solomon Alani, Ibrahim Isa Adamu, Shamtang Benshak Musa "Mathematical Model for The Dynamics of Nutrient-Phytoplankton System with Delay Under Climate Change and Deoxygination of Oceans" Iconic Research And Engineering Journals, vol. 10, no. 1, Jul. 2026, doi: https://doi.org/10.64388/IREV10I1-1719581

APA:
Usman Solomon Alani, Ibrahim Isa Adamu, Shamtang Benshak Musa (2026). Mathematical Model for The Dynamics of Nutrient-Phytoplankton System with Delay Under Climate Change and Deoxygination of Oceans. Iconic Research And Engineering Journals, 10(1). doi: https://doi.org/10.64388/IREV10I1-1719581

MLA:
Usman Solomon Alani, Ibrahim Isa Adamu, Shamtang Benshak Musa "Mathematical Model for The Dynamics of Nutrient-Phytoplankton System with Delay Under Climate Change and Deoxygination of Oceans" Iconic Research And Engineering Journals, vol. 10, no. 1, Jul. 2026. Crossref, https://doi.org/10.64388/IREV10I1-1719581

BibTeX

@article{1719581,
author = {Usman Solomon Alani, Ibrahim Isa Adamu, Shamtang Benshak Musa},
title = {Mathematical Model for The Dynamics of Nutrient-Phytoplankton System with Delay Under Climate Change and Deoxygination of Oceans},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {10},
number = {1},
pages = {793-825},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1719581.pdf},
abstract = {Marine plankton ecosystems are fundamental to global oxygen production and carbon sequestration, yet they are increasingly threatened by ocean deoxygenation, and climate change. This study proposes a novel six-dimensional delayed differential equation model that captures the complex interactions among nutrient concentration (N), phytoplankton biomass (P), zooplankton biomass (Z), dissolved oxygen (O), upper ocean temperature (T), and greenhouse gas concentration (G). Three discrete time delays account for phytoplankton decomposition, zooplankton decomposition, and toxin maturation in phytoplankton. Existence and uniqueness of solutions are established using the Lipschitz condition. Positivity of solutions and boundedness in a positively invariant region are rigorously proved via comparison theorems, while local asymptotic stability of coexistence and temperature-zero equilibria is proven via linearization and the Routh-Hurwitz criteria. Numerical simulations reveal that baseline parameters induce rapid deoxygenation, with dissolved oxygen falling below 0.5 ppm within 15 days despite an initial phytoplankton bloom. Two scenarios sustain high dissolved oxygenation: (i) fixing temperature at 0 °C, which eliminates warming-induced oxygen loss and thermal inhibition of phytoplankton, and (ii) a minimal-deoxygenation case featuring enhanced photosynthetic production, reduced decomposition demand, and efficient greenhouse gas removal. In contrast, moderate and severe deoxygenation scenarios produce hypoxic conditions or complete plankton collapse. Notably, the selected delays (2.5, 4.0, 5.5 days) do not qualitatively alter long-term dynamics compared to delay-free simulations. These findings provide quantitative thresholds for preventing catastrophic dissolved oxygen depletion and highlight the critical roles of thermal stress and nutrient management in preserving marine ecosystem resilience under climate change.},
keywords = {Anoxic, Climate Change, Deoxygenation, Hypoxic, Plankton.},
month = {July}
}