Dynamics of a Virally Infected Phytoplankton and Zooplankton System with Linear Harvesting - Kumar, Rakesh; Kaur, Amanpreet; Das, Krishna Pada; Malik, Ajender Kumar (Journal of Applied Nonlinear Dynamics, 2026)
In this study, we explore an ecological-epidemiological model involving phytoplankton and zooplankton with simultaneous harvesting of all species and a consideration of time delay. We incorporate the Holling type IV functional response to represent interactions between susceptible and infected phytoplankton, while phytoplankton predation is modeled using the Holling type I functional response. A unified harvesting effort (E) is applied to all species. We establish the positivity and boundedness of the solution, conduct feasibility and stability analyses for potential steady states, and investigate the existence of a bionomic equilibrium and an optimal harvesting policy using Pontryagin's maximal principle. Our findings indicate the stability of the trivial steady state when E > BTP (BTP=Biotechnical productivity of phytoplankton), with other states becoming asymptotically stable under specific conditions. A Hopf bifurcation analysis is conducted using harvesting and time delay as bifurcation parameters. Notably, both harvesting and time delay are highly sensitive to system dynamics, capable of inducing chaos. Elevating control parameters, such as the harvesting coefficient and the recovery rate of infected phytoplankton, as well as the growth rate of zooplankton derived from the predation of susceptible phytoplankton, plays a crucial role in stabilizing the system and mitigating chaos. Numerical simulations visually illustrate our theoretical results.