Dynamical Analysis of Nutrient-Phytoplankton-Zooplankton Model with Viral Disease in Phytoplankton Species under Atangana-Baleanu-Caputo Derivative

A mathematical model of the nutrient-phytoplankton-zooplankton associated with viral infection in phytoplankton under the Atangana-Baleanu derivative in Caputo sense is investigated in this study. We prove the theoretical results for the existence and uniqueness of the solutions by using Banach’s and Sadovskii’s fixed point theorems. The notion of various Ulam’s stability is used to guarantee the context of the stability analysis. Furthermore, the equilibrium points and the basic reproduction numbers for the proposed model are provided. The Adams type predictor-corrector algorithm has been applied for the theoretical confirmation to establish the approximate solutions. A variety of numerical plots corresponding to various fractional orders between zero and one are presented to describe the dynamical behavior of the fractional model under consideration.

DIFFUSIVE THREE SPECIES PLANKTON MODEL IN THE PRESENCE OF TOXIC PREY: APPLICATION TO SUNDARBAN MANGROVE WETLAND

The bloom of toxin producing phytoplankton (TPP) is an environmental issue due to its negative impact on fresh water and marine ecology. In this paper, such a phenomenon is modeled using the reaction–diffusion equations. The spatiotemporal interaction among non-toxin producing phytoplankton (NTP), TPP, and zooplankton has been considered with Holling type II and III functional responses. The stability analysis for non-spatial and spatial model system is carried out and numerical simulations are performed for a fixed set of parameter values, which is realistic to planktonic dynamics. It has been observed that on increasing the reduction rate of zooplankton, the system shows cyclic to stable behavior. The result shows that the predators which avoid to toxic prey promote the bloom. Non-Turing patchy pattern has also been observed on time evolution. In this work, we have taken the case study of Sundarban mangrove wetland which is suffering from algal bloom due to the presence of toxic Dinoflagellates and Cyanophyceae. Through the numerical simulation, it has been shown that the higher value of reduction rate of zooplankton ([Formula: see text]) is responsible for bad health of the wetland system.

Harmful algal blooms in fresh and marine water systems: The role of toxin producing phytoplankton

In this paper, we have investigated a model with three interacting species: non-toxic phytoplankton, toxic phytoplankton and zooplankton with Holling type II and III functional responses over the space and time. The role of toxin producing phytoplankton (TPP) has been studied. We have presented the theoretical analysis of pattern formation in spatially distributed population with local diffusion. The paper highlights the heterogeneity of HABs over space and time. The choice of parameter values and the functional response is important to study the effect of TPP, also it would depend more on the nonlinearity of the system. With the help of numerical simulations, we have observed the spatial and spatiotemporal patterns for plankton system. This study demonstrates that TPP plays an important role in controlling the dynamics. We have observed that prey’s anti-predator efforts promote predator switching. It has been found that high predation of TPP helps for the coexistence of toxic, non-toxic phytoplankton and zooplankton population.